Question 405: Atoms & Nuclei

Question

Radius of first orbit in H -atom is ' $a_0$ ' Then, de-Broglie wavelength of electron in the third orbit is

Accepted Answer

$$\begin{aligned}
& 	ext { Radius for } \mathrm{n}^{	ext {th }} 	ext { orbit, } \mathrm{r}_{\mathrm{n}}=\mathrm{a}_0 	imes \mathrm{n}^2 \
& 	ext { For third orbit, } \
& \mathrm{r}_3=\mathrm{a}_0 	imes 3^2 \
& \quad=9 \mathrm{a}_0 \
& 	ext { Also, } \mathrm{mvr}=\frac{\mathrm{nh}}{2 \pi} \
& \Rightarrow \quad \mathrm{mv}=\frac{\mathrm{nh}}{2 \pi \mathrm{r}}=\frac{3 \mathrm{~h}}{2 \pi 	imes 9 \mathrm{a}_0} \
& \lambda=\frac{\mathrm{h}}{\mathrm{mv}}=\frac{\mathrm{h}}{3 \mathrm{~h}} 	imes 2 \pi 	imes 9 \mathrm{a}_0=6 \pi \mathrm{a}_0
\end{aligned}$$

Answer

$3 \pi \mathrm{a}_0$

Answer

$6 \pi \mathrm{a}_0$

Answer

$9 \pi \mathrm{a}_0$

Answer

$12 \pi \mathrm{a}_0$

Atoms & Nuclei

Radius of first orbit in H -atom is ' a_0 ' Then, de-Broglie wavelength of electron in the third orbit is

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