Atomic Structure 1 Question 43
19. According to Bohr’s theory,
$E_{n}=$ Total energy $\quad K_{n}=$ Kinetic energy
$V_{n}=$ Potential energy $\quad r^{n}=$ Radius of $n$th orbit
Match the following :
(2006, 6M)
| Column I | Column II |
|---|---|
| A. $V_{n} / K_{n}=$ ? | p. |
| B. If radius of $n$th orbit $\propto E_{n}^{x}, x=$ ? | q. $\quad-1$ |
| Angular momentum in lowest orbital |
r. -2 |
| D. $\frac{1}{r^{n}} \propto Z^{y}, y=?$ | s. |
Fill in the Blanks
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Answer:
Correct Answer: 19.
Solution:
- A. $V_{n}=-\frac{1}{4 \pi \varepsilon_{0}}\left(\frac{Z e^{2}}{r}\right)$
$$ \begin{aligned} K_{n} & =\frac{1}{8 \pi \varepsilon_{0}}\left(\frac{Z e^{2}}{r}\right) \ \Rightarrow \quad \frac{V_{n}}{K_{n}} & =-2-(\mathrm{r}) \end{aligned} $$
B. $E_{n}=-\frac{Z e^{2}}{8 \pi \varepsilon_{0} r} \propto r^{-1}$
$$ \Rightarrow \quad x=-1-(\mathrm{q}) $$
C. Angular momentum $=\sqrt{l(l+1)} \frac{h}{2 \pi}=0$ in $1 s$-orbital D. $r_{n}=\frac{a_{0} n^{2}}{Z} \Rightarrow \frac{1}{r_{n}} \propto Z-(\mathrm{s})$
