In a diatomic molecule, the inter-nuclear separation of the ground and first excited electronic state are the same as shown in the figure. If the molecule is initially in the lowest vibrational state of the ground state, then the absorption spectrum will appear as <img src="/images/question-image/engineering-physics/atomic-and-molecular-physics/1689658288-in-a-diatomic-molecule-the-inter-nuclear.png" title="Atomic and Molecular Physics mcq question image" alt="Atomic and Molecular Physics mcq question image">

A vibrational-electronic spectrum of homonuclear binary molecules, involving electronic ground state ε'' and excited ε', exhibits a continuum at $$\overline v $$ cm^-1. If the total energy of the dissociated atoms in the excited state exceeds the total energy of the dissociated atoms in the ground state by E_ex cm^-1, then dissociation energy of the molecule in the ground state is

A

$$\frac{{\left( {\overline v + {E_{ex}}} \right)}}{2}$$

B

$$\frac{{\left( {\overline v - {E_{ex}}} \right)}}{2}$$

C

$$\left( {\overline v - {E_{ex}}} \right)$$

D

$$\sqrt {\left( {\overline v - {E_{ex}}^2} \right)} $$

Five energy levels of a system including the ground state are shown below. Their lifetimes and the allowed electric dipole transitions are also marked.

Which one of the following transitions is the most suitable for a Continuous Wave (CW) laser?

A

1 → 0

B

2 → 0

C

4 → 2

D

4 → 3

Two dielectric materials A and B exhibit both ionic and orientational polarizabilities. The variation of their susceptibilities $$\chi \left( { = {\varepsilon _r} - 1} \right)$$ with temperature T is shown in the figure, where $${\varepsilon _r}$$ is the relative dielectric constant. It can be inferred from the figure that

A

A is more polar and it has a smaller value of ionic polarizability than that of B

B

A is more polar and it has a higher value of ionic polarizability than that of B

C

B is more polar and it has a higher value of ionic polarizability than that of A

D

B is more polar and it has a smaller value of ionic polarizability than that of A

The temperature dependence of the electrical conductivity σ of two intrinsic semiconductors A and B is shown in the figure. If E_A and E_B are the band gaps of A and B respectively, which one of the following is true?

A

EA > EB

B

EA B

C

EA = EB

D

EA and EB both depend on temperature

In crystallographic notations, the vector $$\overrightarrow {{\bf{OP}}} $$ in the cubic cell shown in the figure is

A piston containing an ideal gas is originally in the state X (see figure). The gas is taken through a thermal cycle X → Y → X as shown

The work done by the gas is positive, if the direction of the thermal cycle is

A

clockwise

B

counter-clockwise

C

neither clockwise nor counter-clockwise

D

clockwise from X → Y and counter-clockwise from Y → X

The plot of log A vs time t, where A is activity as shown in the figure, corresponds to decay

A

from only one kind of radioactive nuclei having same half life

B

from only neutron activated nuclei

C

from a mixture of radioactive nuclei having different half lives

D

which is unphysical

Variation of electrical resistivity $$\rho $$ with temperature T of three solids is sketched (on different scales) in the figure, as curves P, Q and R.
Which one of the following statements describes the variations most appropriately?

A

P is for a superconductor and R for a semiconductor

B

Q is for a superconductor and P for a conductor

C

Q is for a superconductor and R for a conductor

D

R is for a superconductor and P for a conductor

The dependences of the magnetic susceptibility $$\left( \chi \right)$$ of a material with temperature (T) can be represented by $$\chi \propto \frac{1}{{T - \theta }},$$ where θ is the Curie-Weiss temperature. The plot of magnetic susceptibility versus temperature is sketched in the figure, as curves P, Q and R with curve Q having θ = 0. Which one of the following statements is correct?

A

Curve R represents a paramagnet and Q a ferromagnetic field

B

Curve Q represents a ferromagnet and P an antiferromagnet

C

Curve R represents an antiferromagnet and Q a paramagnet

D

Curve R represents an antiferromagnet and Q a ferromagnet

Consider the figure of a fountain with four holes, given below.

Which one of the holes in the fountain will throw the water farthest?

A

4

B

3

C

2

D

1