Question

Which of the following particles will have same frequency of revolution when projected with same velocity perpendicular to a magnetic field?
1) $L{i}^{++}$
2) $H{e}^{++}$
3) $Proton$
4) $Deuteron$

• A. 1 and 3
• B. 2 and 4
• C. 2 and 3
• D. 1 and 2

Answer 1

The correct option is B

2 and 4

Angular frequency for a charge projected in magnetic field is $\omega =\frac{qB}{m}$
As $B$ is contant,the charge to mass ratio must be same for equal frequency.
The relative values of charge to mass ratio are:
for $L{i}^{++}=\frac{2}{3}$,
for $H{e}^{++}=\frac{2}{4}=\frac{1}{2}$,
for proton $=\frac{1}{1}$ and
for deuteron $=\frac{1}{2}$.
Hence the paths of a deuteron and alpha - particle will be identical and has same frequency.