Problem set 76

1. Which one of the following electronic transitions in neon is NOT responsible for LASER action in a helium-neon laser?
1. $6s\rightarrow5p$
2. $5s\rightarrow4p$
3. $5s\rightarrow3p$
4. $4s\rightarrow3p$

$6s\rightarrow5p$

Hence, answer is (A)

2. In the linear Stark effect, the application of an electric field
1. completely lifts the degeneracy of $n = 2$ level of hydrogen atom and splits $n = 2$ level into four levels
2. partially lifts the degeneracy of $n = 2$ level of hydrogen atom and splits $n = 2$ level into three levels
3. partially lifts the degeneracy of $n = 2$ level of hydrogen atom and splits $n = 2$ level into two levels
4. does not affect the $n= 2$ levels

Partially lifts the degeneracy of $n = 2$ level of hydrogen atom and splits $n = 2$ level into three levels

Hence, answer is (B)

3. In hyperfine interaction, there is coupling between the electron angular momentum $\vec J$ and nuclear angular momentum $\vec I$, forming resultant angular momentum $\vec F$. The selection rules for the corresponding quantum number $F$ in hyperfine transitions are
1. $\Delta F=\pm2$ only
2. $\Delta F=\pm1$ only
3. $\Delta F=0,\pm1$
4. $\Delta F=\pm1,\pm2$

$\Delta F=0,\pm1$

Hence, answer is (C)

4. A vibrational-electronic spectrum of homonuclear binary molecules, involving electronic ground state $\epsilon''$ and excited state $\epsilon'$, exhibits a continuum at $\bar\nu cm^{-1}$. 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 $E_{ex} cm^{-1}$, the dissociation energy of the molecule in the ground state is
1. $(\bar\nu+E_{ex})/2$
2. $(\bar\nu-E_{ex})/2$
3. $(\bar\nu-E_{ex})$
4. $\sqrt{(\bar\nu^2-E_{ex}^2)}$

$D=(\bar\nu-E_{ex})$

Hence, answer is (C)

5. The NMR spectrum of ethanol $(CH_3CH_2OH)$ comprises of three bunches of spectral lines. The number of spectral lines in the bunch corresponding to $CH_2$ group is
1. 1
2. 2
3. 3
4. 4

In ethanol the intensities are in the ratio 3:2:1, because there are three $CH_3$ protons, two $CH_2$ protons and one $OH$ proton in a molecule. So the number of spectral lines in the bunch corresponding to $CH_2$ group is 2

Hence, answer is (B)