Question 527: Atoms & Nuclei

Question

Bohr model is applied to a particle of mass ' $m$ ' and charge ' $q$ ' is moving in a plane under the influence of a transverse magnetic field ' $B$ '. The energy of the charged particle in the $n$th level will be ( $h=$ Planck's constant)

Accepted Answer

For a particle moving in a magnetic field, then applied two forces are equal.
centripetal force $\left(F_cight)=$ magnetic force $\left(F_might)$
$$\begin{aligned}
& \Rightarrow \quad \frac{m v^2}{r}=q v B \
& \Rightarrow \quad m v^2=q B(v r)\quad 	ext{.... (i)}
\end{aligned}$$
Also, from Bohr's model,
$$\begin{aligned}
m v r & =\frac{n h}{2 \pi} \
	herefore \quad v r & =\frac{n h}{2 \pi m}\quad 	ext{.... (ii)}
\end{aligned}$$
From Eq. (i) and (ii), we get
$$m v^2=\frac{n h}{2 \pi m} \cdot q B\quad 	ext{... (iii)}$$
Energy of the electron moving in $n$th orbit,
$$\begin{aligned}
E & =\frac{1}{2} \cdot m v^2=\frac{1}{2} \cdot \frac{n h q B}{2 \pi m} \quad 	ext{(using Eq. (iii)}\
\Rightarrow \quad & E=\frac{n h q B}{4 \pi m}
\end{aligned}$$
Hence, the energy of the charged particle in the $n$th level will be $\frac{n h q B}{4 \pi m}$.

Answer

$2 n h q B / \pi \mathrm{m}$

Answer

$n h q B / 2 \pi \mathrm{~m}$

Answer

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

Answer

$n h q B / \pi \mathrm{m}$

Atoms & Nuclei

Bohr model is applied to a particle of mass ' m ' and charge ' q ' is moving in a plane under the influence of a transverse magnetic field ' B '. The energy of the charged particle in the nth level will be ( h= Planck's constant)

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