11. The 2s-orbital of H-atom has a radial node at 2a0 because $${\psi _{2s}}$$ is proportional to A. $$\left( {\frac{1}{2} + \frac{r}{{{a_0}}}} \right)$$ B. $$\left( {2 + \frac{r}{{{a_0}}}} \right)$$ C. $$\left( {2 - \frac{r}{{{a_0}}}} \right)$$ D. $$\left( {2 - \frac{r}{{2{a_0}}}} \right)$$ Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option C No explanation is given for this question Let's Discuss on Board
12. The region of electromagnetic spectrum employed in the electron spin resonance (ESR) spectroscopy is A. radiowave B. microwave C. infrared D. visible Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option B No explanation is given for this question Let's Discuss on Board
13. Which of the following pairs of operators commute? A. $$x{\text{ and }}\frac{d}{{dx}}$$ B. $$\frac{d}{{dx}}{\text{ and }}\frac{{{d^2}}}{{d{x^2}}} + \frac{{2d}}{{dx}}$$ C. $${x^2}\frac{d}{{dx}}{\text{ and }}\frac{{{d^2}}}{{d{x^2}}}$$ D. $${x^3}{\text{ and }}\frac{d}{{dx}}$$ Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option B No explanation is given for this question Let's Discuss on Board
14. The set of eigen functions $$\sqrt {\frac{2}{a}} \sin \frac{{n\pi x}}{a}\left( {0 \leqslant x \leqslant a,\,n = 1,\,2,\,3,\,...} \right){\text{is}}$$ A. orthogonal B. normalized C. both orthogonal and normalized D. unnormalized Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option C No explanation is given for this question Let's Discuss on Board
15. The system for which energy (E) increases quadratically with the quantum number (n) is A. particle in a one-dimensional box B. hydrogen atom C. one-dimensional harmonic oscillator D. rigid rotor Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option A No explanation is given for this question Let's Discuss on Board
16. The uncertainty in the momentum (Δpx) of the particle in its lowest energy state is A. $$\Delta {p_x} = 0$$ B. $$\Delta {p_x} = \frac{h}{a}$$ C. $$\Delta {p_x} = \frac{h}{{2a}}$$ D. $$\Delta {p_x} = \frac{h}{{2\pi a}}$$ Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option B No explanation is given for this question Let's Discuss on Board
17. 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 A. 2 × 10-4 B. 2 × 10-7 C. 2 × 10-2 D. 0 Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option A No explanation is given for this question Let's Discuss on Board
18. The function eax2 (a > 0) is not an acceptable wave function for bound system because A. it is not continuous B. it is multi-valued C. it is not normalizable D. All of these Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option D No explanation is given for this question Let's Discuss on Board
19. The wave function for a harmonic oscillator described $$Nx\exp \left( { - \frac{{a{x^2}}}{2}} \right)$$ has A. one maximum only B. one maximum, one minimum only C. two maxima, one minimum only D. two maxima, two minima only Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option B No explanation is given for this question Let's Discuss on Board
20. 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 (< px >) of the particle is A. $$ < {p_x} > = 0$$ B. $$ < {p_x} > = \frac{h}{a}$$ C. $$ < {p_x} > = \frac{h}{{2a}}$$ D. $$ < {p_x} > = \frac{h}{{2\pi a}}$$ Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option A No explanation is given for this question Let's Discuss on Board
