Atomic Structure - Result 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. $V _n=-\frac{1}{4 \pi \varepsilon _0}\left(\frac{Z e^{2}}{r}\right)$
$$ \begin{aligned} K _n & =\frac{1}{8 \pi \varepsilon _0}\left(\frac{Z e^{2}}{r}\right) \ \Rightarrow \quad \frac{V _n}{K _n} & =-2-(r) \end{aligned} $$
B. $E _n=-\frac{Z e^{2}}{8 \pi \varepsilon _0 r} \propto r^{-1}$
$$ \Rightarrow \quad x=-1-(q) $$
C. Angular momentum $=\sqrt{l(l+1)} \frac{h}{2 \pi}=0$ in $1 s$-orbital D. $r _n=\frac{a _0 n^{2}}{Z} \Rightarrow \frac{1}{r _n} \propto Z-(s)$
