Problem set 8

1. The 623.8 nm radiation emitted by a He-Ne laser due to the transition between :
1. $3s$ and $2p$ levels of Ne
2. $3s$ and $3p$ levels of Ne
3. $2p$ and $2s$ levels of Ne
4. $2p$ and $1s$ levels of Ne
(A)$3s$ and $2p$ levels of Ne
2. In the Stern-Gerlach experiment, the number of components in which the atomic beam splits depends upon the value of:
1. $l$
2. $s$
3. $j$
4. $m_j$
(C)$j$
3. The Lande's splitting factor for the atomic state $^2P_{3/2}$ is :
1. $1/3$
2. $2/3$
3. $1$
4. $4/3$
For $^2P_{3/2}$ state $(2s+1)=2$, hence $s=1/2$, $j=3/2$, for $P$ state $l=1$ $$\begin{align*} g&={\scriptstyle1+\frac{j(j+1)+s(s+1)-l(l+1)}{2j(j+1)}}\\ &={\scriptstyle1+\frac{\frac{3}{2}(\frac{3}{2}+1)+\frac{1}{2}(\frac{1}{2}+1)-1(1+1)}{2\frac{3}{2}(\frac{3}{2}+1)}}\\ &=\frac{4}{3} \end{align*}$$
4. The "Normal" and "Anomalous" Zeeman effects are observed when (here S' is the total spin angular momentum due to the coupling of individual spin angular momenta)
1. $S'=0$ and $S'\ne0$, respectively
2. $S'=0$ and $S'=0$, respectively
3. $S'\ne0$ and $S'=0$, respectively
4. $S'\ne0$ and $S'\ne0$, respectively
(A)$S'=0$ and $S'\ne0$, respectively
5. The number of photons emitted per second from 1 watt Ar-ion laser operating at 488 nm is approximately
1. $10.23\times10^{19}$
2. $2.46\times10^{18}$
3. $10.23\times10^{17}$
4. $2.46\times10^{15}$
$Power=P=1 watt$, $\lambda=488 ~nm=488\times10^{-9}m$ $$P=NE=Nh\nu=N\frac{hc}{\lambda}$$ $$\begin{align*} N&=P\frac{\lambda}{hc}\\ &=1\times\frac{488\times10^{-9}}{6.63\times10^{-34}\times3\times10^8}\\ &=2.46\times10^{18} \end{align*}$$