Atomic Structure MCQs with Explanations

This question is about the de Broglie wavelength , which tells us that even particles like atoms can behave like waves! The de Broglie wavelength (λ) is calculated using the formula: λ = h/mv where: h is Planck's constant (6.626 x 10 -34 Js) m is the mass of the particle (in kg) v is the velocity of the particle (in m/s) First, we need the mass of a Helium (He) atom. A He atom has a mass of approximately 4 amu (atomic mass units). To use the formula, we need to convert this to kilograms. Since 1 amu ≈ 1.66 x 10 -27 kg, the mass of a He atom is roughly 4 * 1.66 x 10 -27 kg = 6.64 x 10 -27 kg. Now, we can plug the values into the de Broglie wavelength formula: λ = (6.626 x 10 -34 Js) / (6.64 x 10 -27 kg * 1000 m/s) After calculating, you will get a wavelength around 99.7 x 10 -12 m.

The vibrational partition function describes how molecules are distributed among different vibrational energy levels at thermal equilibrium. For a molecule that behaves as a quantum mechanical simple harmonic oscillator , the vibrational energy levels are given by E v = (v + 1/2)hν , where v = 0, 1, 2, ... . When the zero-point energy is treated separately, the vibrational partition function becomes: q vib = 1 / [1 − exp(−hν/k B T)] This expression is equivalent to: q vib = [1 − exp(−hν/k B T)] −1 Therefore, Option B is the correct expression for the vibrational partition function. Why the other options are incorrect: Option A: It contains only the exponential term and is not the complete partition function. Option C: It includes an unnecessary extra exponential factor, so it does not represent the standard vibrational partition function. Option D: It contains the factor exp(−hν/2k B T) , which accounts for the zero-point energy . This form is obtained only when the zero-point energy is explicitly included in the partition function and is not the standard expression generally used in engineering chemistry and statistical thermodynamics.

0.1 (nm)-1/2 is the correct answer to “The wave function for a quantum mechanical particle in a one-dimensional box of length a is given by $$\psi = A\sin \frac{{\pi x}}{a}.$$ The value of A for a box of length 200 nm is”. This question is standard in competitive examination syllabi for Atomic Structure.

$$\Delta \varepsilon _n^{\left( 1 \right)} = 0$$ is the correct answer to “First order perturbation correction $$\Delta \varepsilon _n^{\left( 1 \right)}$$ to energy level $${\varepsilon _n}$$ of a simple harmonic oscillator due to the anharmonicity perturbation $$\gamma {x^3}$$ is given by”. This question is standard in competitive examination syllabi for Atomic Structure.

Bolometer is the correct answer to “Which one of the following is not a photodetector”. This question is standard in competitive examination syllabi for Atomic Structure.

$$\frac{h}{{m{b^2}}}$$ is the correct answer to “An electron of mass m is confined to a one-dimensional box of length b. If it makes a radiative transition from second excited state to the ground state/the frequency of the photon emitted is”. This question is standard in competitive examination syllabi for Atomic Structure.

$$\frac{h}{2}$$ is the correct answer to “As per the uncertainty principle, $$\Delta x \cdot \Delta p$$ equals to”. This question is standard in competitive examination syllabi for Atomic Structure.

5 is the correct answer to “In units of $$\frac{{{h^2}}}{{8m{l^2}}},$$ the energy difference between levels corresponding to 3 and 2 node eigen functions for a particle of mass m in a one-dimensional box of length $$l$$ is”. This question is standard in competitive examination syllabi for Atomic Structure.

decreases with increasing principal quantum number is the correct answer to “The velocity of the electron in the hydrogen atom”. This question is standard in competitive examination syllabi for Atomic Structure.

14.8 × 10-21 J is the correct answer to “The zero-point energy of the vibration of 35 CI 2 mimicking a harmonic oscillator with a force constant k = 2293.8 N/m is”. This question is standard in competitive examination syllabi for Atomic Structure.

$$\left( {2 - \frac{r}{{{a_0}}}} \right)$$ is the correct answer to “The 2s-orbital of H-atom has a radial node at 2a 0 because $${\psi _{2s}}$$ is proportional to”. This question is standard in competitive examination syllabi for Atomic Structure.

microwave is the correct answer to “The region of electromagnetic spectrum employed in the electron spin resonance (ESR) spectroscopy is”. This question is standard in competitive examination syllabi for Atomic Structure.

$$\frac{d}{{dx}}{\text{ and }}\frac{{{d^2}}}{{d{x^2}}} + \frac{{2d}}{{dx}}$$ is the correct answer to “Which of the following pairs of operators commute”. This question is standard in competitive examination syllabi for Atomic Structure.

both orthogonal and normalized is the correct answer to “The set of eigen functions $$\sqrt {\frac{2}{a}} \sin \frac{{n\pi x}}{a}\left( {0 \leqslant x \leqslant a,\,n = 1,\,2,\,3,\,...} \right){\text{is}}$$”. This question is standard in competitive examination syllabi for Atomic Structure.

particle in a one-dimensional box is the correct answer to “The system for which energy (E) increases quadratically with the quantum number (n) is”. This question is standard in competitive examination syllabi for Atomic Structure.

$$\Delta {p_x} = \frac{h}{a}$$ is the correct answer to “The uncertainty in the momentum (Δp x ) of the particle in its lowest energy state is”. This question is standard in competitive examination syllabi for Atomic Structure.

2 × 10-4 is the correct answer to “A particle is confined to a one-dimensional box of length 1 mm. If the length is changed by 10 -9 m, the % change in the ground state energy is”. This question is standard in competitive examination syllabi for Atomic Structure.

All of these is the correct answer to “The function e ax 2 (a > 0) is not an acceptable wave function for bound system because”. This question is standard in competitive examination syllabi for Atomic Structure.

one maximum, one minimum only is the correct answer to “The wave function for a harmonic oscillator described $$Nx\exp \left( { - \frac{{a{x^2}}}{2}} \right)$$ has”. This question is standard in competitive examination syllabi for Atomic Structure.

$$ < {p_x} > = 0$$ is the correct answer to “Consider a particle of mass m moving in a one-dimensional box under the potential V = 0 for 0 ≤ x ≤ a and V = $$\infty $$ outside the box. When the particle is in its lowest energy state, the average momentum (< p x >) of the particle is”. This question is standard in competitive examination syllabi for Atomic Structure.