Question 482: Atoms & Nuclei

Question

Bohr model is applied to a particle of mass '$$\mathrm{m}$$' and charge '$$\mathrm{q}$$' moving in a plane under the influence of a transverse magnetic field '$$B$$'. The energy of the charged particle in the $$\mathrm{n}^{	ext {th }}$$ leve will be $$[\mathrm{h}=$$ Planck's constant $$]$$

Accepted Answer

We know,
$$\begin{aligned}
\mathrm{mvr} & =\frac{\mathrm{nh}}{2 \pi} \
	herefore \quad \mathrm{vr} & =\frac{\mathrm{nh}}{2 \pi \mathrm{m}}\quad 	ext{.... (i)}
\end{aligned}$$
Also,
$$\begin{aligned}
& \mathrm{qvB}=\frac{\mathrm{mv}^2}{\mathrm{r}} \
& 	herefore \quad \mathrm{mv}=\mathrm{qBr} \quad 	ext{.... (ii)}\
& \mathrm{mv}^2 \mathrm{r}=\mathrm{qBr} 	imes \frac{\mathrm{nh}}{2 \pi \mathrm{m}}  \quad 	ext{....(Multiplying (i) with (ii))}\
& \mathrm{E}=\frac{1}{2} \mathrm{mv}^2=\mathrm{n}\left[\frac{\mathrm{qBh}}{4 \pi \mathrm{m}}ight]
\end{aligned}$$

Answer

$$\frac{n h q B}{4 \pi \mathrm{m}}$$

Answer

$$\frac{n h q B}{2 \pi m}$$

Answer

$$\frac{	ext { nhqB }}{\pi \mathrm{m}}$$

Answer

$$\frac{2 \mathrm{nhqB}}{\pi \mathrm{m}}$$

Atoms & Nuclei

Bohr model is applied to a particle of mass '$\mathrm{m}' and charge '\mathrm{q}' moving in a plane under the influence of a transverse magnetic field 'B'. The energy of the charged particle in the \mathrm{n}^{\text {th }} leve will be [\mathrm{h}= Planck's constant ]

Choose the correct answer: