Atomic Structure - Result Question 19
Match the Columns
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
(2006, 6M)
Match the following :
| Column I | Column II | ||
|---|---|---|---|
| A. | $V _n / K _n=$ ? | p. | 0 |
| B. | If radius of $n$th orbit $\propto E _n^{x}, x=$ ? | q. | -1 |
| C. | Angular momentum in lowest orbital |
r. | -2 |
| D. | $\dfrac{1}{r^{n}} \propto Z^{y}, y=?$ | s. | 1 |
Show Answer
Answer:
Correct Answer: 19. $ A \rightarrow r; \hspace{2mm} B \rightarrow q; \hspace{2mm} C \rightarrow p; \hspace{2mm} D \rightarrow s $
Solution:
- A. $V _n=-\dfrac{1}{4 \pi \varepsilon _0}\left(\dfrac{Z e^{2}}{r}\right)$
$ \begin{aligned} K _n & =\dfrac{1}{8 \pi \varepsilon _0}\left(\dfrac{Z e^{2}}{r}\right) \\ \Rightarrow \quad \dfrac{V _n}{K _n} & =-2 \quad -(r) \end{aligned} $
B. $E _n=-\dfrac{Z e^{2}}{8 \pi \varepsilon _0 r} \propto r^{-1}$
$ \Rightarrow \quad x=-1 \quad -(q) $
C. Angular momentum $=\sqrt{l(l+1)} \dfrac{h}{2 \pi}=0$ in $1 s$-orbital $\quad -(p)$
D. $r _n=\dfrac{a _0 n^{2}}{Z} \Rightarrow \dfrac{1}{r _n} \propto Z \quad -(s)$
BETA
