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Atoms Set-3 MCQ Online Practice Test | Class 12 | Quiz Tweek

Atoms Set-3

Practice Important MCQs for Atoms — Physics, Class 12.

The chapter "Atoms" connects classical ideas and quantum concepts to explain atomic spectra, quantised energy levels, and microscopic properties of matter. Mastery of this chapter helps in solving numerical problems (Rydberg formula, Bohr radii, reduced-mass corrections) and in interpreting wavefunction-based results (radial probability, nodes) — skills that are heavily tested in both CBSE board papers and competitive exams (JEE/NEET).

Beyond routine calculations, the chapter trains students to interpret experimental data (spectral series, isotopic shifts), reason about selection rules and operator properties, and reconcile Bohr-model intuition with quantum mechanical wavefunctions. These abilities are essential for tackling multi-step problems, graph interpretation, and assertion–reason type questions frequently seen in exams.

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Q1. An electron in a hydrogen atom makes a transition from $n=3$ to $n=2$ . Using $R_\infty=1.097\times10^{7}\ \mathrm{m^{-1}}$ , the wavelength of the emitted photon is closest to:

(A)

A: $4.86\times10^{-7}\ \mathrm{m}$

(B)

B: $1.216\times10^{-7}\ \mathrm{m}$

(C)

C: $6.56\times10^{-7}\ \mathrm{m}$

(D)

D: $1.875\times10^{-6}\ \mathrm{m}$

Q2. For a hydrogen atom with proton mass $m_p=1836\,m_e$ , the reduced mass is $\mu=\dfrac{m_e m_p}{m_e+m_p}$ and the effective Rydberg constant is $R=R_\infty\dfrac{\mu}{m_e}$ . The numerical value of $\dfrac{R}{R_\infty}$ is approximately:

(A)

A: $0.99990$

(B)

B: $0.99946$

(C)

C: $0.99800$

(D)

D: $1.00000$

Q3. Assertion (A): In the Bohr model for a hydrogen-like atom the orbital speed obeys $v_n\propto 1/n$ , hence $v_{n+1}/v_n=\dfrac{n}{n+1}$ .
Reason (R): From $m v r = n\hbar$ and $r\propto n^2$ one obtains $v\propto 1/n$ , which explains the assertion.

(A)

A: Both A and R are true, and R is the correct explanation for A.

(B)

B: Both A and R are true, but R is not the correct explanation for A.

(C)

C: A is true but R is false.

(D)

D: A is false but R is true.

Q4. Consider the radial probability density $P(r)=|R_{nl}(r)|^2 r^2$ for hydrogen. Two curves are plotted: Curve I has $P(0)\neq0$ , shows one radial node and two maxima (one near $r\sim a_0$ and another at larger $r$ ). Curve II has $P(0)=0$ and a single maximum near $r\sim4a_0$ . Which statement correctly identifies the curves and a consequent property?

(A)

A: Curve I corresponds to $2p$ and Curve II to $2s$ ; hence $2p$ has nonzero probability at the nucleus.

(B)

B: Curve I corresponds to $1s$ and Curve II to $2p$ ; the $1s$ state has a radial node.

(C)

C: Curve I corresponds to $2s$ and Curve II to $2p$ ; the $2s$ state has a smaller mean radius $\langle r\rangle$ than $2p$ .

(D)

D: Curve I corresponds to $2s$ and Curve II to $2p$ ; the $2s$ state has a larger probability density near the nucleus than the $2p$ state.

Q5. Using Bohr radius $a_0=5.29\times10^{-11}\ \mathrm{m}$ , the de Broglie wavelength of the electron in the ground state ( $n=1$ ) of hydrogen is:

(A)

A: $5.29\times10^{-11}\ \mathrm{m}$

(B)

B: $3.32\times10^{-10}\ \mathrm{m}$

(C)

C: $1.05\times10^{-10}\ \mathrm{m}$

(D)

D: $6.28\times10^{-9}\ \mathrm{m}$

Q6. Consider hydrogen (H, $Z=1$ ) and the helium ion He $^+$ ( $Z=2$ ) each with an electron in the ground state. Neglect nuclear recoil. Which of the following is correct?

(A)

A: For He $^+$ , $r_1$ is half that of H ( $r_{1}^{\mathrm{He^+}}=\tfrac{1}{2}r_{1}^{\mathrm{H}}$ ), the binding energy magnitude is $4$ times that of H, and the electron's de Broglie wavelength is halved.

(B)

B: For He $^+$ , $r_1$ is half that of H, binding energy magnitude is $4$ times, but the de Broglie wavelength is the same as H.

(C)

C: For He $^+$ , $r_1$ equals that of H, binding energy magnitude is $4$ times, and the de Broglie wavelength is halved.

(D)

D: For He $^+$ , $r_1$ is one-fourth that of H, binding energy magnitude is $2$ times, and de Broglie wavelength is quartered.

Q7. Assertion (A): Allowed electric dipole transitions in an atom obey the selection rule $\Delta l=\pm1$ .
Reason (R): This selection rule follows because the dipole operator $\mathbf{r}$ behaves like a spherical harmonic of rank zero ( $Y_0^0$ ) under rotations, so it conserves $l$ .

(A)

A: Both A and R are true and R is the correct explanation.

(B)

B: Both A and R are true but R is not the correct explanation.

(C)

C: A is true but R is false.

(D)

D: A is false but R is true.

Q8. An experimental plot of wavenumber $1/\lambda$ versus $(1/n_f^2-1/n_i^2)$ for several observed lines of a hydrogen-like ion is a straight line through the origin with slope $4.388\times10^{7}\ \mathrm{m^{-1}}$ . Taking $R_\infty=1.097\times10^{7}\ \mathrm{m^{-1}}$ and neglecting reduced-mass corrections, the nuclear charge $Z$ of the ion is closest to:

(A)

A: $1$

(B)

B: $\sqrt{2}$

(C)

C: $3$

(D)

D: $2$

Q9. Compare photon energies for two transitions: (i) hydrogen $n=4\to2$ , and (ii) helium ion He $^+$ $n=3\to1$ (assume infinite nuclear mass). The ratio $E_{\mathrm{He^+}}/E_{\mathrm{H}}$ is approximately:

(A)

A: $9.5$

(B)

B: $19$

(C)

C: $4$

(D)

D: $0.5$

Q10. A muonic hydrogen atom is formed when the electron is replaced by a muon of mass $m_\mu=207\,m_e$ . Taking proton mass $m_p=1836\,m_e$ , estimate the ground-state binding energy magnitude $|E_1|$ and Bohr radius $a_1$ of muonic hydrogen. Choose the closest pair $(|E_1|,\ a_1)$ :

(A)

A: $|E_1|\approx 2.53\times10^{3}\ \mathrm{eV},\quad a_1\approx 2.84\times10^{-13}\ \mathrm{m}$

(B)

B: $|E_1|\approx 1.36\times10^{4}\ \mathrm{eV},\quad a_1\approx 5.29\times10^{-12}\ \mathrm{m}$

(C)

C: $|E_1|\approx 7.4\times10^{-2}\ \mathrm{eV},\quad a_1\approx 1.0\times10^{-9}\ \mathrm{m}$

(D)

D: $|E_1|\approx 2.53\times10^{2}\ \mathrm{eV},\quad a_1\approx 2.84\times10^{-12}\ \mathrm{m}$

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