1. $n=3\text{,}l=1\text{,}\mathbf{or}\mathbf{a}3pstate$.

2. You can see in Figure 41.7  that the ns state has $n$ maxima.

3. No. $m_s=\pm \frac{1}{2}$, so the z-component $S_z$ cannot be zero.

4. b. The atom would have less energy if the $3s$ electron were in a $2p$ state.

5. c. Emission is a quantum jump to a lower-energy state. The $5p\to 4p$ transition is not allowed because $\text{Δ}l=0$ violates the selection rule. The lowest-energy allowed transition is $5p\to 3d$, with $E_{\text{photon}}=\text{Δ}{E}_{\text{atom}}=3.0\text{eV}$.

6. b. Because $r_{\text{B}}=2r_{\text{A}},\text{ the ratio is}{e}^{-2}/e^{-1}=e^{-1}<\frac{1}{2}$.

1.

1. $\left(3\text{,}1\text{,}1\right)\text{,}\left(3\text{,}1\text{,}0\right)\text{,}(3\text{,}1,-1)$

2. $\left(3\text{,}2\text{,}2\right)\text{,}\left(3\text{,}2\text{,}1\right)\text{,}\left(3\text{,}2\text{,}0\right)\text{, }(3\text{,}2,-1)\text{,}(3\text{,}2,-2)$

3. $\sqrt{20}\hslash$

5.

1. $f$

2. $-0.850\text{eV}$

7. $\begin{array}{l}\text{For }n=1\text{, 2 states: }(\text{1, 0, 0, }\pm {\displaystyle \frac{1}{2}})\text{;}\\ \text{for }n=2\text{, 8 states: }(\text{2, 0, 0, }\pm {\displaystyle \frac{1}{2}}),\\ (\text{2,}1\text{,}-1\text{, }\pm {\displaystyle \frac{1}{2}}),(\text{2, 1, 0, }\pm {\displaystyle \frac{1}{2}})\text{,}(\text{2, 1, 1, }\pm {\displaystyle \frac{1}{2}})\text{;}\\ \text{for }n=3\text{, 18 states: }(\text{3, 0, 0, }\pm {\displaystyle \frac{1}{2}})\text{,}(\text{3, 1, }-1\text{, }\pm {\displaystyle \frac{1}{2}}),\\ (\text{3, 1, 0, }\pm {\displaystyle \frac{1}{2}})\text{,}(\text{3, 1, 1, }\pm {\displaystyle \frac{1}{2}})\text{,}(\text{3, 2, 2, }\pm {\displaystyle \frac{1}{2}}),\\ (\text{3, 2, 1, }\pm {\displaystyle \frac{1}{2}})\text{,}(\text{3, 2, 0, }\pm {\displaystyle \frac{1}{2}})\text{,}(\text{3, 2, }-1\text{, }\pm {\displaystyle \frac{1}{2}})\text{,}(\text{3, 2, }-2\text{, }\pm {\displaystyle \frac{1}{2}})\end{array}$

9. $\begin{array}{l}1s^{2}2s^{2}2p^{6}3s^{2}3p\text{, }1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p,\\ 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p^{6}5s^{2}4d^{10}5p\end{array}$

11.

1. Excited state of Ne

2. Ground state of Ti

13.

15. $1s^{2}3s$

17.

19. 2.0%

21. 27 ns

23.

1. $1.06\mu \text{m}$

2. 1.9 W

25.

1. 190 nm

2. 50 kW

27.

• a. $\sqrt{2}\hslash$

• b. $-1\text{,}0,\text{ or}1$

• c.

  

  Full Alternative Text

29. $\sqrt{6}\hslash$

31.

1. $3.7\times {10}^{-3}$

2. $5.4\times {10}^{-3}$

3. $2.9\times {10}^{-3}$

37.

1. $L{}_z$	$S{}_z$	$J{}_z$	$m{}_j$
   $\hslash$	$+\frac{1}{2}\hslash$	$\frac{3}{2}\hslash$	$\frac{3}{2}$
   $\hslash$	$-\frac{1}{2}\hslash$	$\frac{1}{2}\hslash$	$\frac{1}{2}$
   0	$+\frac{1}{2}\hslash$	$\frac{1}{2}\hslash$	$\frac{1}{2}$
   0	$-\frac{1}{2}\hslash$	$-\frac{1}{2}\hslash$	$-\frac{1}{2}$
   $-\hslash$	$+\frac{1}{2}\hslash$	$-\frac{1}{2}\hslash$	$-\frac{1}{2}$
   $-\hslash$	$-\frac{1}{2}\hslash$	$-\frac{3}{2}\hslash$	$-\frac{3}{2}$

2. $j=\frac{1}{2}\text{: }(\frac{1}{2}\hslash \text{, }-\frac{1}{2}\hslash )$, $j=\frac{3}{2}\text{: }(\frac{3}{2}\hslash \text{,}\frac{1}{2}\hslash \text{, }-\frac{1}{2}\hslash \text{, }-\frac{3}{2}\hslash )$

39. 4.59 eV

41.

43.

1. Transition	$\text{Δ}E(\text{eV})$	$\text{λ}(\text{nm})$
   $6p\to 6s$	6.70	185
   $6d\to 6p$	2.14	579
   $7s\to 6p$	1.22	1016
   $7p\to 6s$	8.84	140
   $7p\to 7s$	0.92	1350
   $8s\to 6p$	2.52	492
   $8s\to 7p$	0.38	3260
   $8p\to 6s$	9.53	130
   $8p\to 7s$	1.61	770
   $8p\to 8s$	0.31	4000
   $8p\to 6d$	0.69	1800

2. $1.80\times {10}^6\text{m}\text{/}\text{s}$

45.

• a.

  

  Full Alternative Text

• b. 28.7 eV

47.

1. $6.3\times {10}^8\text{s}{}^{-1}$

2. 0.17 ns

49. $3.5\times {10}^{18}\text{atoms}$

51.

1. $p_{\text{atom}}=7.0\times {10}^{-23}\text{kg}\text{m/s}\text{;}{p}_{\text{photon}}=-8.50\times {10}^{-28}\text{kg}\text{m/s}$

2. $82\times {10}^3\text{photons}$

3. 1.2 ms

4. $-5.7\times {10}^{-20}\text{N, }-4/0\times {10}^5\text{m}\text{/}{\text{s}}^2$

5. 31 cm

53. b. 0.021 nm

57. 5.7 ns