Modern Physics Ques 165
- An electron in an excited state of $Li^{2+}$ ion has angular momentum $\frac{3 h}{2 \pi}$. The de Broglie wavelength of the electron in this state is $p \pi a _0$ (where $a _0$ is the Bohr radius). The value of $p$ is
(2015 Adv.)
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Answer:
Correct Answer: 165.$(2)$
Solution:
Formula:
Radius And Speed Of Electron In Hydrogen Like Atoms:
- Angular momentum $=n (\frac{h}{2 \pi})=3 (\frac{h}{2 \pi})$
$ \therefore \quad n=3 $
Now, $r _n \propto \frac{n^{2}}{z}$
$\therefore \quad r _3=\frac{(3)^{2}}{3}\left(a _0\right)=3 a _0$
Now, $m v _3 r _3=3 (\frac{h}{2 \pi})$
$\therefore \quad m v _3\left(3 a _0\right)=3 (\frac{h}{2 \pi})$
or $\quad \frac{h}{m v _3}=2 \pi a _0\quad $ or $\quad \frac{h}{P _3}=2 \pi a _0 \quad(\because P=m v)$
or $\quad \lambda _3=2 \pi a _0\quad $ $(\lambda=\frac{h}{P})$
$\therefore \quad$ Answer is $2$ .
BETA
