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
Answer: Option
C
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
Answer: Option
B
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
Answer: Option
B
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
Answer: Option
C
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
Answer: Option
A
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
Answer: Option
B
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
Answer: Option
A
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
Answer: Option
D
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
Answer: Option
B
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
Answer: Option
A
