Timer: Off
Random: Off
201. Who proposed the dual nature of matter, introducing the concept of matter waves?
ⓐ. Albert Einstein
ⓑ. Louis de Broglie
ⓒ. Niels Bohr
ⓓ. Max Planck
Correct Answer: Louis de Broglie
Explanation: In 1924, de Broglie suggested that just as light shows wave–particle duality, electrons and all matter also have wave properties. His hypothesis was later confirmed by electron diffraction experiments.
202. According to de Broglie, the wavelength of a particle is given by:
ⓐ. $\lambda = \dfrac{E}{h}$
ⓑ. $\lambda = \dfrac{h}{p}$
ⓒ. $\lambda = \dfrac{hc}{E}$
ⓓ. $\lambda = \dfrac{p}{h}$
Correct Answer: $\lambda = \dfrac{h}{p}$
Explanation: The de Broglie wavelength is inversely proportional to momentum. For mass $m$ and velocity $v$: $$\lambda = \dfrac{h}{mv}$$
203. What experimental evidence confirmed de Broglie’s hypothesis?
ⓐ. Rutherford’s gold foil experiment
ⓑ. Davisson–Germer electron diffraction experiment
ⓒ. Millikan’s oil drop experiment
ⓓ. Young’s double-slit experiment with light
Correct Answer: Davisson–Germer electron diffraction experiment
Explanation: In 1927, Davisson and Germer observed diffraction of electrons by a nickel crystal, proving electrons exhibit wave-like behavior consistent with de Broglie’s theory.
204. The de Broglie wavelength of an electron accelerated through potential $V$ is:
ⓐ. $\lambda = \dfrac{h}{\sqrt{2meV}}$
ⓑ. $\lambda = \dfrac{h}{meV}$
ⓒ. $\lambda = \dfrac{eV}{h}$
ⓓ. $\lambda = \dfrac{hc}{eV}$
Correct Answer: $\lambda = \dfrac{h}{\sqrt{2meV}}$
Explanation: Kinetic energy of electron = $eV$. Momentum $p = \sqrt{2meV}$. Hence, $\lambda = \dfrac{h}{p} = \dfrac{h}{\sqrt{2meV}}$.
205. What happens to the de Broglie wavelength of a particle if its velocity increases?
ⓐ. Wavelength increases
ⓑ. Wavelength decreases
ⓒ. Wavelength remains constant
ⓓ. Wavelength becomes infinite
Correct Answer: Wavelength decreases
Explanation: Since $\lambda = \dfrac{h}{mv}$, increasing velocity increases momentum, which reduces wavelength.
206. Which principle is closely related to the wave nature of matter proposed by de Broglie?
ⓐ. Pauli’s exclusion principle
ⓑ. Heisenberg’s uncertainty principle
ⓒ. Archimedes’ principle
ⓓ. Pascal’s principle
Correct Answer: Heisenberg’s uncertainty principle
Explanation: Wave nature implies that position and momentum cannot both be precisely determined. This idea supports Heisenberg’s uncertainty principle.
207. For a stationary electron, the de Broglie wavelength is:
ⓐ. Infinite
ⓑ. Zero
ⓒ. Equal to its Compton wavelength
ⓓ. Cannot be defined
Correct Answer: Infinite
Explanation: If velocity = 0, momentum = 0, so $\lambda = \dfrac{h}{0}$, which tends to infinity. Thus, stationary particles have infinite de Broglie wavelength.
208. The concept of standing electron waves inside the atom was used by:
ⓐ. Bohr to explain quantized angular momentum
ⓑ. Sommerfeld to explain elliptical orbits
ⓒ. Schrödinger to explain wave functions
ⓓ. De Broglie to explain quantized orbits
Correct Answer: De Broglie to explain quantized orbits
Explanation: De Broglie suggested that electrons in atoms behave like standing waves. Only those orbits are allowed where the electron wavelength fits an integer number of times along the orbit circumference.
209. Which formula represents the condition for allowed electron orbits according to de Broglie?
ⓐ. $2\pi r = n\lambda$
ⓑ. $2r = n\lambda$
ⓒ. $r = n\lambda$
ⓓ. $2\pi r = \dfrac{\lambda}{n}$
Correct Answer: $2\pi r = n\lambda$
Explanation: De Broglie explained Bohr’s quantization by requiring that the circumference of an orbit equals an integer multiple of the electron’s wavelength: $$2\pi r = n\lambda$$
210. The wave–particle duality of electron means:
ⓐ. Electrons behave only like particles
ⓑ. Electrons behave only like waves
ⓒ. Electrons can show both wave-like and particle-like behavior
ⓓ. Electrons cannot be detected experimentally
Correct Answer: Electrons can show both wave-like and particle-like behavior
Explanation: De Broglie’s hypothesis established that electrons and all matter have dual character: they exhibit wave-like properties (diffraction, interference) and particle-like properties (collisions, photoelectric effect).
211. Heisenberg’s uncertainty principle relates to the simultaneous measurement of:
ⓐ. Energy and charge
ⓑ. Position and momentum
ⓒ. Mass and velocity
ⓓ. Time and temperature
Correct Answer: Position and momentum
Explanation: The principle states that it is impossible to simultaneously determine the exact position $x$ and momentum $p$ of a particle with absolute certainty. Their uncertainties are inversely related.
212. The mathematical expression of the uncertainty principle is:
ⓐ. $\Delta x \cdot \Delta p \geq \dfrac{h}{4\pi}$
ⓑ. $\Delta x \cdot \Delta p \geq h$
ⓒ. $\Delta x \cdot \Delta p \leq \dfrac{h}{4\pi}$
ⓓ. $\Delta x \cdot \Delta p = 0$
Correct Answer: $\Delta x \cdot \Delta p \geq \dfrac{h}{4\pi}$
Explanation: The exact inequality states that the product of the uncertainties in position and momentum is at least $h/4\pi$. This sets a fundamental limit, not due to measurement error but due to the wave nature of particles.
213. According to the uncertainty principle, increasing the accuracy of measuring a particle’s position will:
ⓐ. Increase accuracy of momentum measurement
ⓑ. Decrease accuracy of momentum measurement
ⓒ. Not affect momentum measurement
ⓓ. Stop the particle from moving
Correct Answer: Decrease accuracy of momentum measurement
Explanation: Since $\Delta x \cdot \Delta p \geq \dfrac{h}{4\pi}$, reducing $\Delta x$ forces $\Delta p$ to increase. Thus, the more precisely we know the position, the less precisely we know the momentum.
214. Which of the following phenomena can be explained using the uncertainty principle?
ⓐ. Stability of atoms
ⓑ. Reflection of light
ⓒ. Refraction of light
ⓓ. Dispersion of light
Correct Answer: Stability of atoms
Explanation: Electrons do not collapse into the nucleus because confining them to a very small space would give them very high momentum (kinetic energy). This uncertainty provides stability to atoms.
215. Which quantities are related by the time–energy form of uncertainty principle?
ⓐ. Time and temperature
ⓑ. Time and kinetic energy
ⓒ. Time interval and uncertainty in energy
ⓓ. Time interval and uncertainty in position
Correct Answer: Time interval and uncertainty in energy
Explanation: The time–energy uncertainty relation is $\Delta E \cdot \Delta t \geq \dfrac{h}{4\pi}$. This explains, for example, natural line broadening in spectral lines.
216. If uncertainty in position of an electron is reduced, what happens to the uncertainty in its momentum?
ⓐ. Decreases
ⓑ. Increases
ⓒ. Remains constant
ⓓ. Becomes zero
Correct Answer: Increases
Explanation: By the principle, a smaller $\Delta x$ forces a larger $\Delta p$. Hence precision in one variable worsens precision in the other.
217. Heisenberg’s uncertainty principle is a direct consequence of:
ⓐ. Wave–particle duality of matter
ⓑ. Newton’s laws of motion
ⓒ. Coulomb’s law
ⓓ. Conservation of mass
Correct Answer: Wave–particle duality of matter
Explanation: Because particles like electrons also behave like waves, their exact position and momentum cannot be simultaneously defined, leading to the uncertainty principle.
218. Which of the following statements about the uncertainty principle is incorrect?
ⓐ. It is due to limitations of experimental apparatus.
ⓑ. It is a fundamental property of quantum systems.
ⓒ. It cannot be avoided even with better instruments.
ⓓ. It applies to microscopic particles like electrons.
Correct Answer: It is due to limitations of experimental apparatus.
Explanation: The uncertainty principle is not about measurement errors but a fundamental property of quantum particles. Even with perfect instruments, the uncertainty relation holds.
219. In classical mechanics, both position and momentum can be measured exactly. Why not in quantum mechanics?
ⓐ. Because quantum particles move randomly
ⓑ. Because electrons have no definite mass
ⓒ. Because wave nature introduces fundamental uncertainty
ⓓ. Because Planck’s constant is very large
Correct Answer: Because wave nature introduces fundamental uncertainty
Explanation: In quantum mechanics, matter waves extend in space, so precise position and momentum cannot be simultaneously defined. Planck’s constant is small, but non-zero, which makes uncertainty significant at atomic scales.
220. Which of the following is a correct implication of the uncertainty principle?
ⓐ. Electrons revolve in fixed circular paths
ⓑ. Orbits of electrons are replaced by orbitals
ⓒ. Atoms collapse due to electron attraction
ⓓ. Momentum of particles is always zero
Correct Answer: Orbits of electrons are replaced by orbitals
Explanation: Bohr’s model assumed exact electron orbits, which violate the uncertainty principle. In modern quantum mechanics, electrons are described by orbitals (probability distributions) instead of definite paths.
221. Who formulated the wave equation that describes the behavior of an electron in an atom?
ⓐ. Niels Bohr
ⓑ. Louis de Broglie
ⓒ. Erwin Schrödinger
ⓓ. Werner Heisenberg
Correct Answer: Erwin Schrödinger
Explanation: In 1926, Schrödinger developed the wave equation for matter waves. It describes how the wave function $\psi$ of an electron evolves in space and time, forming the foundation of quantum mechanics.
222. The Schrödinger wave equation gives information about:
ⓐ. Exact path of an electron
ⓑ. Probability distribution of an electron in space
ⓒ. Energy of nucleus
ⓓ. Mass of proton
Correct Answer: Probability distribution of an electron in space
Explanation: The square of the wave function, $|\psi|^2$, gives the probability density of finding an electron at a particular point. It replaces the idea of fixed orbits with orbitals.
223. The time-independent Schrödinger equation is written as:
ⓐ. $\dfrac{d^2\psi}{dx^2} + \dfrac{8\pi^2m}{h^2}(E – V)\psi = 0$
ⓑ. $E = mc^2$
ⓒ. $\Delta x \cdot \Delta p \geq \dfrac{h}{4\pi}$
ⓓ. $p = \dfrac{h}{\lambda}$
Correct Answer: $\dfrac{d^2\psi}{dx^2} + \dfrac{8\pi^2m}{h^2}(E – V)\psi = 0$
Explanation: The time-independent Schrödinger equation in one dimension expresses how the wave function $\psi$ relates to total energy $E$, potential energy $V$, and mass $m$.
224. The quantity $|\psi|^2$ in Schrödinger’s equation represents:
ⓐ. Velocity of electron
ⓑ. Charge of electron
ⓒ. Angular momentum of electron
ⓓ. Probability density of electron Charge of electron
Correct Answer: Probability density of electron
Explanation: Schrödinger interpreted $|\psi|^2$ as the probability density for finding a particle in a particular region of space. This probabilistic interpretation replaced the deterministic orbits of Bohr’s model.
225. Which concept replaced Bohr’s fixed orbits due to Schrödinger’s work?
ⓐ. Orbitals
ⓑ. Energy shells
ⓒ. Nuclear paths
ⓓ. Quantum fields
Correct Answer: Orbitals
Explanation: Schrödinger’s wave mechanics introduced orbitals — regions in space where the probability of finding an electron is highest. This solved the conflict with Heisenberg’s uncertainty principle.
226. Which type of equation is Schrödinger’s wave equation?
ⓐ. Algebraic equation
ⓑ. Differential equation
ⓒ. Polynomial equation
ⓓ. Exponential equation
Correct Answer: Differential equation
Explanation: Schrödinger’s wave equation is a second-order linear differential equation. It describes the variation of the wave function in space and time under given energy conditions.
227. Which of the following quantum numbers emerge from solving Schrödinger’s equation for the hydrogen atom?
ⓐ. Principal, Azimuthal, Magnetic
ⓑ. Only Principal
ⓒ. Only Spin
ⓓ. All four including Spin
Correct Answer: Principal, Azimuthal, Magnetic
Explanation: Solving Schrödinger’s equation yields three quantum numbers: $n, l, m_l$. The spin quantum number $m_s$ was introduced separately by Pauli.
228. What physical meaning does the wave function $\psi$ itself have?
ⓐ. Directly measurable physical property
ⓑ. No direct physical meaning, only $|\psi|^2$ has physical significance
ⓒ. Represents the orbit of the electron
ⓓ. Represents angular momentum of the electron
Correct Answer: No direct physical meaning, only $|\psi|^2$ has physical significance
Explanation: The wave function $\psi$ may be positive or negative and cannot be directly measured. The measurable probability density is given by $|\psi|^2$.
229. Which principle is naturally incorporated into Schrödinger’s wave mechanics?
ⓐ. Newton’s third law
ⓑ. Bohr’s quantization postulate
ⓒ. Heisenberg’s uncertainty principle
ⓓ. Coulomb’s law
Correct Answer: Heisenberg’s uncertainty principle
Explanation: Schrödinger’s approach does not give precise electron paths but probability distributions, aligning with the uncertainty principle that forbids exact knowledge of both position and momentum.
230. Which statement about Schrödinger’s wave equation is correct?
ⓐ. It is applicable only to hydrogen atom.
ⓑ. It can be solved exactly only for hydrogen-like systems.
ⓒ. It cannot explain atomic spectra.
ⓓ. It proves electrons revolve in circular orbits.
Correct Answer: It can be solved exactly only for hydrogen-like systems.
Explanation: The Schrödinger equation can be exactly solved for hydrogen and hydrogen-like species (He$^+$, Li$^{2+}$, etc.). For multi-electron systems, approximate methods are used due to electron–electron interactions.
231. In Bohr’s atomic model, an orbit refers to:
ⓐ. A probability distribution of electrons around the nucleus
ⓑ. A region in space where finding electron is uncertain
ⓒ. A circular path with definite radius and energy
ⓓ. A set of overlapping electron wave functions
Correct Answer: A circular path with definite radius and energy
Explanation: In Bohr’s model, electrons move in fixed circular orbits around the nucleus with definite energy and radius. This view is classical and contradicts the uncertainty principle.
232. In quantum mechanics, an orbital is defined as:
ⓐ. Exact trajectory of an electron
ⓑ. A fixed circular path around nucleus
ⓒ. The central part of nucleus only
ⓓ. A three-dimensional region with high probability of finding electron
Correct Answer: A three-dimensional region with high probability of finding electron
Explanation: An orbital describes the electron cloud distribution in 3D space where the probability of locating an electron is maximum, represented by $|\psi|^2$.
233. Which of the following is NOT true about atomic orbitals?
ⓐ. They are described by quantum numbers
ⓑ. They represent regions of space with probability distribution
ⓒ. They are definite paths of electron revolution
ⓓ. They arise as solutions of Schrödinger equation
Correct Answer: They are definite paths of electron revolution
Explanation: Orbitals are not fixed paths but probability clouds. Orbits (Bohr’s idea) suggested circular paths, which quantum mechanics rejected.
234. Which model introduced the concept of atomic orbitals instead of fixed orbits?
ⓐ. Rutherford’s nuclear model
ⓑ. Bohr’s planetary model
ⓒ. Schrödinger’s wave mechanical model
ⓓ. Thomson’s plum pudding model
Correct Answer: Schrödinger’s wave mechanical model
Explanation: Schrödinger replaced Bohr’s orbits with orbitals derived from the wave equation. Orbitals represent allowed energy states as electron clouds.
235. Which quantum number primarily determines the size of an orbital?
ⓐ. Spin quantum number
ⓑ. Magnetic quantum number
ⓒ. Azimuthal quantum number
ⓓ. Principal quantum number
Correct Answer: Principal quantum number
Explanation: The principal quantum number $n$ determines the size and energy of an orbital. Higher $n$ means larger orbital size and higher energy.
236. The shape of an orbital is determined by which quantum number?
ⓐ. Principal ($n$)
ⓑ. Spin ($m_s$)
ⓒ. Azimuthal ($l$)
ⓓ. Magnetic ($m_l$)
Correct Answer: Azimuthal ($l$)
Explanation: The azimuthal quantum number $l$ determines orbital shape: $l=0$ (spherical s), $l=1$ (dumbbell p), $l=2$ (clover d), etc.
237. Which of the following best explains the difference between orbit and orbital?
ⓐ. Orbit is 3D, orbital is 2D
ⓑ. Orbit follows uncertainty, orbital does not
ⓒ. Orbit is fixed circular path, orbital is probability region
ⓓ. Orbit relates to quantum mechanics, orbital relates to classical mechanics
Correct Answer: Orbit is fixed circular path, orbital is probability region
Explanation: Orbit (Bohr) = fixed path; Orbital (Schrödinger) = region of high probability. This shift solved the conflict with uncertainty principle.
238. In Bohr’s theory, electrons revolve in orbits because:
ⓐ. Centrifugal force balances electrostatic attraction
ⓑ. Neutrons push electrons outward
ⓒ. Orbitals trap electrons probabilistically
ⓓ. Orbits are generated from wave functions
Correct Answer: Centrifugal force balances electrostatic attraction
Explanation: Bohr’s model assumed circular motion due to balance between Coulomb force (inward) and centrifugal force (outward). Quantum mechanics replaced this with probability-based orbitals.
239. Which concept is compatible with Heisenberg’s uncertainty principle?
ⓐ. Orbit
ⓑ. Orbital
ⓒ. Both orbit and orbital
ⓓ. Neither orbit nor orbital
Correct Answer: Orbital
Explanation: Orbit requires precise position and momentum, violating uncertainty. Orbital gives only probability density, consistent with the uncertainty principle.
240. Which of the following statements about orbitals is correct?
ⓐ. Orbital gives exact path of an electron
ⓑ. Orbital has well-defined energy and probability distribution
ⓒ. Orbitals can never overlap or hybridize
ⓓ. Orbitals are always spherical in shape
Correct Answer: Orbital has well-defined energy and probability distribution
Explanation: Each orbital corresponds to a quantized energy state with a probability cloud. Not all orbitals are spherical (p, d, f have varied shapes), and they can overlap or hybridize in molecules.
241. What is an atomic orbital?
ⓐ. A fixed circular path in which electron moves around nucleus
ⓑ. A three-dimensional region where probability of finding an electron is maximum
ⓒ. A line spectrum obtained from an excited atom
ⓓ. The total number of protons inside nucleus
Correct Answer: A three-dimensional region where probability of finding an electron is maximum
Explanation: An orbital represents the region in space around the nucleus where an electron is most likely to be found. It is defined by the square of the wave function, $|\psi|^2$.
242. The number of atomic orbitals in the $n^{th}$ shell is given by:
ⓐ. $n$
ⓑ. $2n$
ⓒ. $2n^2$
ⓓ. $n^2$
Correct Answer: $n^2$
Explanation: For a given principal quantum number $n$, the total number of orbitals available is $n^2$. For example, $n=2$ gives 4 orbitals (2s, 2p$_x$, 2p$_y$, 2p$_z$).
243. The maximum number of electrons that can be accommodated in an orbital is:
ⓐ. 1
ⓑ. 2
ⓒ. 4
ⓓ. $2n^2$
Correct Answer: 2
Explanation: According to Pauli’s exclusion principle, an orbital can hold a maximum of two electrons, and they must have opposite spins.
244. Which quantum number determines the shape of an orbital?
ⓐ. Principal quantum number ($n$)
ⓑ. Azimuthal quantum number ($l$)
ⓒ. Magnetic quantum number ($m_l$)
ⓓ. Spin quantum number ($m_s$)
Correct Answer: Azimuthal quantum number ($l$)
Explanation: The shape of orbitals (s, p, d, f) is determined by the azimuthal quantum number. For example, $l=0$ gives spherical s orbitals, $l=1$ gives dumbbell-shaped p orbitals.
245. Which orbital is spherical in shape?
ⓐ. p-orbital
ⓑ. d-orbital
ⓒ. s-orbital
ⓓ. f-orbital
Correct Answer: s-orbital
Explanation: The s-orbitals ($l=0$) are spherical around the nucleus. p-orbitals are dumbbell-shaped, d-orbitals are cloverleaf, and f-orbitals have more complex shapes.
246. The orientation of an orbital in space is given by:
ⓐ. Principal quantum number ($n$)
ⓑ. Magnetic quantum number ($m_l$)
ⓒ. Azimuthal quantum number ($l$)
ⓓ. Spin quantum number ($m_s$)
Correct Answer: Magnetic quantum number ($m_l$)
Explanation: The magnetic quantum number specifies how an orbital is oriented in three-dimensional space relative to the other orbitals.
247. The concept of orbitals replaced the concept of orbits because:
ⓐ. Electrons cannot be detected in atoms
ⓑ. Bohr’s orbits violated Heisenberg’s uncertainty principle
ⓒ. Orbitals have no physical meaning
ⓓ. Atoms do not contain electrons
Correct Answer: Bohr’s orbits violated Heisenberg’s uncertainty principle
Explanation: Orbitals describe probability clouds instead of fixed paths, making them consistent with the uncertainty principle.
248. The energy of an orbital depends mainly on:
ⓐ. $n$ only
ⓑ. $n$ and $l$
ⓒ. $n$ and $m_l$
ⓓ. $n$ and $m_s$
Correct Answer: $n$ and $l$
Explanation: In multi-electron atoms, orbital energy depends on principal quantum number $n$ and azimuthal quantum number $l$. For example, 4s is lower in energy than 3d.
249. Which of the following is NOT a correct statement about orbitals?
ⓐ. Orbitals are regions where electrons are likely to be found
ⓑ. Orbitals have distinct shapes and orientations
ⓒ. Orbitals can overlap in chemical bonding
ⓓ. Orbitals represent exact paths of electrons
Correct Answer: Orbitals represent exact paths of electrons
Explanation: Orbitals are probability regions, not fixed paths. Exact electron trajectories are forbidden by uncertainty principle.
250. In Schrödinger’s model, the mathematical function $\psi$ describes:
ⓐ. The shape of the orbital directly
ⓑ. The mass of the electron
ⓒ. The wave function of the electron
ⓓ. The spin direction of the electron
Correct Answer: The wave function of the electron
Explanation: Schrödinger’s equation yields the wave function $\psi$. While $\psi$ itself has no direct physical meaning, $|\psi|^2$ gives the probability density, describing orbitals.
251. Which statement correctly describes Bohr’s concept of an orbit?
ⓐ. It is a probability distribution for an electron.
ⓑ. It is a fixed circular path with definite radius and energy.
ⓒ. It is a 3D wave function solution.
ⓓ. It is a region of maximum electron probability.
Correct Answer: It is a fixed circular path with definite radius and energy.
Explanation: In Bohr’s model, electrons revolve around the nucleus in fixed circular paths called orbits. These orbits had definite radius and energy, which contradicted later quantum mechanics.
252. Which statement correctly defines an orbital?
ⓐ. A fixed 2D path for electrons.
ⓑ. A probability cloud describing where electrons are most likely found.
ⓒ. A circular trajectory of an electron.
ⓓ. A region determined only by nucleus.
Correct Answer: A probability cloud describing where electrons are most likely found.
Explanation: Orbitals arise from Schrödinger’s equation. They are regions in space with high probability of electron presence, not exact paths.
253. Why was the concept of orbit replaced by orbital?
ⓐ. Orbit did not satisfy Coulomb’s law.
ⓑ. Orbit predicted electrons have no charge.
ⓒ. Orbit predicted elliptical paths only.
ⓓ. Orbit violated Heisenberg’s uncertainty principle.
Correct Answer: Orbit violated Heisenberg’s uncertainty principle.
Explanation: Orbits required exact knowledge of both position and momentum of an electron, which is impossible. Orbitals, based on probability, are consistent with uncertainty.
254. Which feature is unique to orbitals but not to orbits?
ⓐ. Defined by principal quantum number only.
ⓑ. Determined by classical mechanics.
ⓒ. Always circular and fixed in radius.
ⓓ. Determined by quantum numbers $n, l, m_l$.
Correct Answer: Determined by quantum numbers $n, l, m_l$.
Explanation: Orbitals are specified by three quantum numbers (shape, size, orientation). Bohr’s orbits were based only on $n$.
255. In Bohr’s orbit, electrons are assumed to:
ⓐ. Radiate energy continuously.
ⓑ. Revolve without radiation in stationary paths.
ⓒ. Exist only as waves without mass.
ⓓ. Occupy 3D probability clouds.
Correct Answer: Revolve without radiation in stationary paths.
Explanation: Bohr postulated stationary orbits where electrons do not radiate energy. Radiation occurs only during jumps between orbits.
256. Which is NOT a characteristic of orbitals?
ⓐ. They describe regions of electron probability.
ⓑ. They have different shapes (s, p, d, f).
ⓒ. They are exact circular tracks of electrons.
ⓓ. They can overlap in chemical bonding.
Correct Answer: They are exact circular tracks of electrons.
Explanation: Orbitals are not fixed paths; they are probability distributions. Their shapes depend on $l$, e.g., spherical s, dumbbell p, cloverleaf d.
257. Which physical concept is better explained by orbitals than orbits?
ⓐ. Emission of continuous spectrum.
ⓑ. Line spectra of hydrogen.
ⓒ. Shapes and orientations of electron regions.
ⓓ. Rutherford scattering of alpha particles.
Correct Answer: Shapes and orientations of electron regions.
Explanation: Orbitals give the 3D shapes and orientations of electron clouds, crucial for bonding and molecular structure. Bohr’s orbits could not explain these.
258. In Bohr’s orbit model, angular momentum of an electron is quantized as:
ⓐ. $mvr = n\hbar$
ⓑ. $mvr = nh$
ⓒ. $mvr = n^2h$
ⓓ. $mvr = \dfrac{h}{2n}$
Correct Answer: $mvr = n\hbar$
Explanation: Bohr proposed quantization of angular momentum: $mvr = n\dfrac{h}{2\pi} = n\hbar$. This is consistent with de Broglie’s standing wave idea.
259. Which statement distinguishes orbitals from orbits in terms of dimensionality?
ⓐ. Orbitals are 1D paths; orbits are 3D clouds.
ⓑ. Both are strictly 2D in nature.
ⓒ. Orbitals are 2D surfaces; orbits are 4D functions.
ⓓ. rbitals are 3D regions; orbits are 1D circular paths.
Correct Answer: Orbitals are 3D regions; orbits are 1D circular paths.
Explanation: Orbits are circular trajectories (1D paths) around nucleus. Orbitals are 3D regions of probability derived from wave functions.
260. Which of the following statements is correct?
ⓐ. Orbit explains uncertainty, orbital violates it.
ⓑ. Orbital concept is based on Schrödinger’s equation, orbit is based on Bohr’s postulates.
ⓒ. Orbitals are fixed circular tracks, orbits are 3D probability distributions.
ⓓ. Orbitals and orbits mean the same.
Correct Answer: Orbital concept is based on Schrödinger’s equation, orbit is based on Bohr’s postulates.
Explanation: Orbitals arise from solving Schrödinger’s equation, giving quantum numbers and probability distributions. Orbits were introduced by Bohr using semi-classical assumptions.
261. Which orbital has a spherical shape around the nucleus?
ⓐ. p-orbital
ⓑ. d-orbital
ⓒ. f-orbital
ⓓ. s-orbital
Correct Answer: s-orbital
Explanation: All s-orbitals ($l=0$) are perfectly spherical in shape, with electron density equally distributed around the nucleus. Higher s-orbitals (2s, 3s, etc.) only differ in size and have radial nodes.
262. The three dumbbell-shaped orbitals oriented along x, y, and z axes are:
ⓐ. s-orbitals
ⓑ. p-orbitals
ⓒ. d-orbitals
ⓓ. f-orbitals
Correct Answer: p-orbitals
Explanation: p-orbitals ($l=1$) are dumbbell-shaped, oriented along x, y, z axes ($p_x, p_y, p_z$). Each can hold 2 electrons, giving 6 electrons total in p-subshell.
263. How many d-orbitals exist in a given shell?
ⓐ. 3
ⓑ. 5
ⓒ. 7
ⓓ. 9
Correct Answer: 5
Explanation: For $l=2$, there are 5 possible orbitals ($m_l = -2, -1, 0, +1, +2$). These orbitals (like $d_{xy}, d_{xz}, d_{yz}, d_{x^2-y^2}, d_{z^2}$) have cloverleaf or special shapes.
264. The maximum number of electrons in a p-subshell is:
ⓐ. 2
ⓑ. 4
ⓒ. 6
ⓓ. 8
Correct Answer: 6
Explanation: A p-subshell has 3 orbitals, each accommodating 2 electrons with opposite spins. Hence, maximum = $3 \times 2 = 6$.
265. Which quantum number decides the number of orbitals in a subshell?
ⓐ. Principal quantum number ($n$)
ⓑ. Azimuthal quantum number ($l$)
ⓒ. Magnetic quantum number ($m_l$)
ⓓ. Spin quantum number ($m_s$)
Correct Answer: Magnetic quantum number ($m_l$)
Explanation: For a given $l$, $m_l$ values range from $-l$ to $+l$, giving $2l+1$ orbitals. Example: $l=1$ → 3 orbitals in p-subshell.
266. Which statement about orbitals is correct?
ⓐ. Orbitals are fixed circular paths around nucleus
ⓑ. Orbitals represent 3D regions of electron probability
ⓒ. All orbitals are spherical in shape
ⓓ. Orbitals cannot overlap during bonding
Correct Answer: Orbitals represent 3D regions of electron probability
Explanation: Orbitals arise from Schrödinger’s wave function. They are not fixed paths but electron probability regions. Only s-orbitals are spherical; others differ in shapes.
267. The number of orbitals present in the 3rd shell ($n=3$) is:
ⓐ. 3
ⓑ. 6
ⓒ. 9
ⓓ. 18
Correct Answer: 9
Explanation: The total number of orbitals in any shell is $n^2$. For $n=3$, we have $3^2 = 9$ orbitals (1 in 3s, 3 in 3p, 5 in 3d).
268. The shape of f-orbitals is generally described as:
ⓐ. Complex multi-lobed
ⓑ. Dumbbell
ⓒ. Spherical
ⓓ. Cloverleaf
Correct Answer: Complex multi-lobed
Explanation: f-orbitals ($l=3$) have very complex shapes with multiple lobes. They are important in the chemistry of lanthanides and actinides.
269. The orientation of p-orbitals in space is given by:
ⓐ. Principal quantum number
ⓑ. Magnetic quantum number
ⓒ. Azimuthal quantum number
ⓓ. Spin quantum number
Correct Answer: Magnetic quantum number
Explanation: The 3 orientations of p-orbitals ($p_x, p_y, p_z$) are determined by $m_l$ values ($-1, 0, +1$). This defines the orientation in space.
270. Which subshell can have a maximum of 14 electrons?
ⓐ. p-subshell
ⓑ. d-subshell
ⓒ. s-subshell
ⓓ. f-subshell
Correct Answer: f-subshell
Explanation: f-subshell ($l=3$) has 7 orbitals, each holding 2 electrons. Thus, maximum capacity = $7 \times 2 = 14$.
271. The principal quantum number ($n$) primarily describes:
ⓐ. Shape of orbital
ⓑ. Orientation of orbital
ⓒ. Size and energy of orbital
ⓓ. Spin of electron
Correct Answer: Size and energy of orbital
Explanation: The principal quantum number indicates the main energy level of an electron. Larger $n$ means larger orbital size and higher energy.
272. For a given value of $n$, the maximum number of electrons that can be accommodated is:
ⓐ. $n^2$
ⓑ. $2n$
ⓒ. $2n^2$
ⓓ. $n^3$
Correct Answer: $2n^2$
Explanation: Each orbital can hold 2 electrons, and the number of orbitals in a shell = $n^2$. Therefore, maximum electrons = $2n^2$.
273. If $n=3$, how many orbitals are possible in that shell?
ⓐ. 3
ⓑ. 6
ⓒ. 7
ⓓ. 9
Correct Answer: 9
Explanation: Number of orbitals in a shell = $n^2$. For $n=3$, there are 9 orbitals (3s, 3p$_x$, 3p$_y$, 3p$_z$, 5 in 3d).
274. The energy of an electron in the hydrogen atom is proportional to:
ⓐ. $-1/n^2$
ⓑ. $1/n$
ⓒ. $+n$
ⓓ. $n^2$
Correct Answer: $-1/n^2$
Explanation: The energy of the hydrogen atom in the nth orbit is $E_n = -\dfrac{13.6}{n^2}\,\text{eV}$. The negative sign shows that the electron is bound to the nucleus.
275. Which shell corresponds to $n=4$?
ⓐ. L-shell
ⓑ. M-shell
ⓒ. N-shell
ⓓ. O-shell
Correct Answer: N-shell
Explanation: Shells are denoted as: $n=1$ → K, $n=2$ → L, $n=3$ → M, $n=4$ → N, and so on.
276. What is the total number of orbitals in the second shell ($n=2$)?
ⓐ. 2
ⓑ. 4
ⓒ. 6
ⓓ. 8
Correct Answer: 4
Explanation: For $n=2$, $n^2=4$ orbitals exist: one 2s orbital and three 2p orbitals.
277. If an electron is in $n=1$ shell, it is in which orbital?
ⓐ. 1p
ⓑ. 1d
ⓒ. 3d
ⓓ. 1s
Correct Answer: 1s
Explanation: The first shell ($n=1$) contains only one orbital: 1s. Higher orbitals (p, d, f) start appearing from $n=2$ onwards.
278. Which of the following increases as the principal quantum number increases?
ⓐ. Nuclear charge
ⓑ. Penetration power of orbital
ⓒ. Average distance of electron from nucleus
ⓓ. Number of protons in the atom
Correct Answer: Average distance of electron from nucleus
Explanation: As $n$ increases, electrons are farther from the nucleus, orbital size increases, and binding energy decreases.
279. For $n=3$, how many subshells are present?
ⓐ. 2
ⓑ. 3
ⓒ. 4
ⓓ. 5
Correct Answer: 3
Explanation: For any $n$, subshells = $l = 0$ to $(n-1)$. For $n=3$: $l=0$ (s), $l=1$ (p), $l=2$ (d). Hence, 3 subshells.
280. Which of the following is correct about the principal quantum number?
ⓐ. It determines only the spin of electron.
ⓑ. It is always zero or positive.
ⓒ. It can have any positive integer value starting from 1.
ⓓ. It has values between $-\infty$ to $+\infty$.
Correct Answer: It can have any positive integer value starting from 1.
Explanation: The principal quantum number $n = 1, 2, 3,\dots$. It cannot be zero or negative. It defines main shells in an atom.
281. The azimuthal quantum number $l$ primarily determines the:
ⓐ. Orientation of an orbital in space
ⓑ. Principal energy level of the electron
ⓒ. Subshell type and shape of the orbital
ⓓ. Spin of the electron
Correct Answer: Subshell type and shape of the orbital
Explanation: The azimuthal (angular momentum) quantum number $l$ labels subshells (s, p, d, f …) and governs their shapes. For $l=0,1,2,3$, the subshells are s, p, d, f respectively. It also influences angular nodes (equal to $l$). Orientation is set by $m_l$, while principal energy level is given by $n$, and spin by $m_s$.
282. For the shell $n=4$, the possible values of $l$ are:
ⓐ. $0,1,2,3$
ⓑ. $1,2,3,4$
ⓒ. $0,1,2,3,4$
ⓓ. $2,3,4,5$
Correct Answer: $0,1,2,3$
Explanation: For any shell $n$, $l$ can take integer values $0$ to $n-1$. Thus for $n=4$, $l\in\{0,1,2,3\}$. These correspond to 4s, 4p, 4d, and 4f subshells. No value of $l$ equals or exceeds $n$.
283. How many orbitals are present in a subshell with $l=2$?
ⓐ. 2
ⓑ. 3
ⓒ. 4
ⓓ. 5
Correct Answer: 5
Explanation: The number of orbitals in a subshell is $2l+1$. For $l=2$ (d-subshell), $2l+1=5$ orbitals exist: $d_{xy}, d_{yz}, d_{xz}, d_{x^2-y^2}, d_{z^2}$. Each orbital can hold 2 electrons, so the subshell can accommodate up to 10 electrons.
284. The maximum number of electrons that a p-subshell can hold is:
ⓐ. 4
ⓑ. 6
ⓒ. 8
ⓓ. 10
Correct Answer: 6
Explanation: For p ($l=1$), there are $2l+1=3$ orbitals ($p_x, p_y, p_z$). Each orbital holds 2 electrons with opposite spins, giving $3\times2=6$. In general, a subshell can hold $2(2l+1)=4l+2$ electrons.
285. Which letter notation corresponds to $l=3$?
ⓐ. s
ⓑ. p
ⓒ. f
ⓓ. d
Correct Answer: f
Explanation: The mapping is $l=0\to$s, $1\to$p, $2\to$d, $3\to$f, $4\to$g, etc. Thus $l=3$ denotes an f-subshell, characterized by complex multi-lobed shapes and up to 7 orbitals.
286. The magnitude of orbital angular momentum for a given $l$ is:
ⓐ. $L = l\,h$
ⓑ. $L = l\,\hbar$
ⓒ. $L = \dfrac{h}{2\pi l}$
ⓓ. $L = \sqrt{l(l+1)}\,\hbar$
Correct Answer: $L = \sqrt{l(l+1)}\,\hbar$
Explanation: Quantum mechanics gives $\lVert \mathbf{L} \rVert = \sqrt{l(l+1)}\,\hbar$. This arises from the eigenvalues of $\hat{L}^2$. The simpler $l\hbar$ is only the $z$-component magnitude step size (via $m_l$), not the total magnitude.
287. The number of angular nodes in an orbital equals:
ⓐ. $l$
ⓑ. $n-l-1$
ⓒ. $n-1$
ⓓ. $2l+1$
Correct Answer: $l$
Explanation: Angular nodes are determined solely by $l$. For example, any p-orbital ($l=1$) has one angular node (a nodal plane). Radial nodes depend on both $n$ and $l$ via $n-l-1$, and total nodes are $n-1$.
288. For a hydrogen-like atom (one electron), energy of an orbital depends on:
ⓐ. $l$ only
ⓑ. $n$ only (degenerate in $l$)
ⓒ. $n$ and $l$ equally
ⓓ. $l$ and $m_l$ only
Correct Answer: $n$ only (degenerate in $l$)
Explanation: In hydrogenic systems, all subshells with the same $n$ have the same energy (Coulomb potential is purely $1/r$). In multi-electron atoms, electron–electron repulsion and shielding break this degeneracy, making energy depend on $n$ and $l$.
289. The allowed magnetic quantum numbers $m_l$ for $l=2$ are:
ⓐ. $-1,0,+1$
ⓑ. $0, +1, +2$
ⓒ. $-2,-1,0$
ⓓ. $-2,-1,0,+1,+2$
Correct Answer: $-2,-1,0,+1,+2$
Explanation: For a given $l$, $m_l$ takes all integer values from $-l$ to $+l$. With $l=2$, there are five orientations consistent with the $2l+1$ orbitals of the d-subshell.
290. The number of radial nodes in a 4d orbital is:
ⓐ. 0
ⓑ. 2
ⓒ. 1
ⓓ. 3
Correct Answer: 1
Explanation: Radial nodes are given by $n-l-1$. For 4d, $n=4$ and $l=2$, so radial nodes $=4-2-1=1$. Total nodes are $n-1=3$, thus angular nodes $=l=2$ and radial nodes $=1$.
291. The magnetic quantum number ($m_l$) describes:
ⓐ. The size of an orbital
ⓑ. The shape of an orbital
ⓒ. The orientation of an orbital in space
ⓓ. The spin of an electron
Correct Answer: The orientation of an orbital in space
Explanation: $m_l$ defines the orientation of an orbital relative to the x, y, z axes. For example, $p_x, p_y, p_z$ orbitals correspond to $m_l = -1, 0, +1$ when $l=1$.
292. For a subshell with $l=2$, the possible values of $m_l$ are:
ⓐ. $-2, -1, 0, +1, +2$
ⓑ. $-1, 0, +1$
ⓒ. $0, +1, +2$
ⓓ. $-3, -2, -1, 0, +1, +2, +3$
Correct Answer: $-2, -1, 0, +1, +2$
Explanation: For any $l$, $m_l$ takes values from $-l$ to $+l$. So for $l=2$, we get 5 values: $-2, -1, 0, +1, +2$, corresponding to the five d-orbitals.
293. The number of orbitals in a subshell is given by:
ⓐ. $2n^2$
ⓑ. $2l+1$
ⓒ. $n^2$
ⓓ. $4l+2$
Correct Answer: $2l+1$
Explanation: Each value of $m_l$ corresponds to one orbital. For a given $l$, there are $2l+1$ possible values of $m_l$, meaning that many orbitals in the subshell.
294. How many orbitals are present in the p-subshell?
ⓐ. 1
ⓑ. 2
ⓒ. 3
ⓓ. 5
Correct Answer: 3
Explanation: For p-subshell, $l=1$, so $m_l$ = $-1, 0, +1$. This gives 3 orbitals ($p_x, p_y, p_z$), each accommodating 2 electrons, for a total of 6 electrons.
295. If $l=3$, how many orientations of orbitals are possible?
ⓐ. 5
ⓑ. 6
ⓒ. 10
ⓓ. 7
Correct Answer: 7
Explanation: Number of possible orbitals = $2l+1$. For $l=3$ (f-subshell), $2(3)+1 = 7$. Thus, 7 orientations are possible.
296. The value of $m_l$ is associated with:
ⓐ. Spin angular momentum
ⓑ. Orbital angular momentum projection along z-axis
ⓒ. Principal energy level of an electron
ⓓ. Radial distribution of electron
Correct Answer: Orbital angular momentum projection along z-axis
Explanation: $m_l$ determines the component of orbital angular momentum along the z-axis. This affects orientation of orbitals in an external magnetic field.
297. If $l=0$, what is the only possible value of $m_l$?
ⓐ. 0
ⓑ. +1
ⓒ. -1
ⓓ. -2
Correct Answer: 0
Explanation: For s-orbital ($l=0$), $m_l$ can only take a single value: 0. This means s-orbitals are spherically symmetric with no directional preference.
298. The splitting of spectral lines in a magnetic field is explained by:
ⓐ. Pauli’s exclusion principle
ⓑ. Zeeman effect
ⓒ. Hund’s rule
ⓓ. Stark effect
Correct Answer: Zeeman effect
Explanation: The Zeeman effect is splitting of spectral lines under a magnetic field, caused by the interaction of magnetic moments (from $m_l$) with the external field.
299. How many orbitals are present in the d-subshell?
ⓐ. 3
ⓑ. 4
ⓒ. 7
ⓓ. 5
Correct Answer: 5
Explanation: For d-subshell, $l=2$, so $m_l$ ranges from $-2$ to $+2$, giving 5 orbitals. Each orbital can hold 2 electrons, for a total of 10 electrons.
300. The values of $m_l$ indicate:
ⓐ. The energy of electron in a multi-electron atom
ⓑ. The allowed orientations of orbitals in space
ⓒ. The spin of electron
ⓓ. The wavelength of light emitted by the atom
Correct Answer: The allowed orientations of orbitals in space
Explanation: $m_l$ tells how orbitals are oriented relative to coordinate axes. For example, p-orbitals are oriented along x, y, and z axes. It does not directly determine electron spin or wavelength.
In Class 11 Chemistry, the chapter Structure of Atom plays a critical role in developing a deep understanding of atomic structure and electron distribution. Aligned with the NCERT/CBSE syllabus, it explores the application of quantum numbers in defining electron positions, shapes of orbitals (s, p, d, f), and the method of writing electronic configurations using Aufbau’s principle, Pauli’s exclusion principle, and Hund’s rule. These concepts are frequently tested in board exams and are a core part of competitive exams like JEE and NEET. With a total of 475 MCQs divided into 5 parts, this chapter ensures comprehensive coverage for practice. This section provides the third set of 100 solved MCQs, helping you strengthen problem-solving and application skills. Use the part buttons and navigation links above to continue exploring more questions or switch chapters.
- 👉 Total MCQs in this chapter: 475 (5 parts).
- 👉 This page contains: Third set of 100 solved MCQs.
- 👉 Designed for board exam practice and JEE/NEET aspirants.
- 👉 For more chapters, subjects, or classes, use the navigation bar above.
- 👉 To access the next part, click the Part 4 button above.