Problem set 65

1. What are the expected types of gamma ray transitions between the following states of odd ‘A’ nuclei : $$f_{5/2}\rightarrow P_{3/2}$$
1. E3, M4, E5, M6
2. M1, E2, M3, E4
3. M4, E5, M6, E7
4. M4, M1, E3, E4

Gamma rays emitted in electric $E$-$l$ transitions carry off angular momentum $l$ and parity $(-1)^l$. Therefore, angular momenta and parity of final and initial states are related by $$\Delta I=|I_i-I_f| \text{ to } I_i-I_f=l$$ $$\text{and }\Delta\pi=(-1)^l$$ The selection rules for magnetic $M$-$l$ transitions are $$\Delta I=|I_i-I_f|\text{ to } I_i-I_f=l$$ $$\text{and }\Delta\pi=(-1)^{l-1}$$ Following table shows selections rules for $\gamma$-ray transitions

Type	$l=\Delta I$	$\Delta\pi$
E1	1	yes
M1	1	no
E2	2	no
M2	2	yes
E3	3	yes
M3	3	no
E4	4	no
M4	4	yes
E5	5	yes
M5	5	no

For $f_{5/2}\rightarrow P_{3/2}$ $$\Delta I=l=\left|\frac{5}{2}-\frac{3}{2}\right|\text{ to } \frac{5}{2}+\frac{3}{2}$$ $$\Delta I=l=1,2,3,4$$ Also, we know that the state with even $l$ value have even parity and the state with odd $l$ have odd parity. Hence, for $f_{5/2}$ parity is odd and for $P_{3/2}$ parity is odd. Hence, there is no parity change i.e. $$\Delta\pi=\text{ no}$$ For $l=1,2,3,4$ and $\Delta\pi=\text{ no}$, from above table we get that transitions as M1, E2, M3 and E4

Hence, answer is (B)

2. Which of the following molecules will not be sensitive to microwave spectroscopy?
1. $LiH$
2. $CO$
3. $CH_4$
4. $CCl_3$

Microwave spectrum can not be observed for centrosymmetric linear molecules such as $N_2$ (dinitrogen) or HCCH (ethyne), which are non-polar. Tetrahedral molecules such as $CH_4$ (methane), which have both a zero dipole moment and isotropic polarizability, would not have a pure rotation spectrum.

Hence, answer is (C)

3. Based on the additive quantum numbers such as strangeness, Baryon number, charge of the particle and Isospin, indicate the following nuclear reaction cannot be induced with the following combination: $$\pi^++n\rightarrow \pi^0+k^+$$
1. Q, B, S are conversed, but $I_3$ is not conserved
2. Q, B are conversed, but S, $I_3$ are not conserved
3. Q, $I_3$ are conversed, but B, S are not conserved
4. B, S, $I_3$ are conversed, but Q is not conserved

	$\pi^++n\rightarrow \pi^0+k^+$
Q	$1+0\rightarrow 0+1$	Conserved
B	$0+1\rightarrow 0+0 $	Not Conserved
S	$0+0\rightarrow 0+1$	Not Conserved
$I_3$	$1+\frac{1}{2}\rightarrow 1+\frac{1}{2}$	Conserved

Hence, answer is (C)

4. Ripple factor is defined as the ratio between :
1. $V_{ac}V_{dc}$
2. $V_{ac}/V_{dc}$
3. $V_{dc}/V_{ac}$
4. $V_{in}/V_{out}$

Ripple factor is defined as the ratio of the root mean square (rms) value of the ripple voltage to the absolute value of the DC component of the output voltage.

Hence, answer is (B)

5. Magnetic moment of duteron $\mu_D\ne \mu_p+\mu_n$. This is due to:
1. Spin dependence of nuclear force
2. Tensor character of nuclear force
3. Spin-orbit force part of nuclear force
4. Hard core part of the nuclear force

The deuteron consists of a neutron and a proton. The deuteron is known to have a quadrupole moment, 0.00286 barns, which tells us that the deuteron is not perfectly spherical and that the force between two nucleons is not spherically symmetric. The force between two nucleons has two components, a spherically symmetric central force and an asymmetric tensor force that depends on the angles between the spin axis of each nucleon and the line connecting.

Hence, answer is (B)