Question

Singly ionized helium(x), ionized deuteron(y), alpha(z) particles are projected into a uniform magnetic field $3\times {10}^{-4}$ Tesla with velocities ${10}^{5}m{s}^{-1}$, $0.4\times {10}^{4}m{s}^{-1}$ and $2\times {10}^{3}m{s}^{-1}$ respectively. The correct relation between the ratio of the angular momentum to the magnetic moment of the particles is :

• A. $x>y=z$
• B. $x<y<z$
• C. $x<z<y$
• D. $z>x>y$

Answer 1

Answer: (A)

$x>y=z$

The magnetic moment of the particle is given by $M=\frac{qL}{2m}$

thus rearranging

$\frac{L}{M}=\frac{2m}{q}$

So, $\frac{L}{M}\alpha \frac{m}{q}$

For deuteron and alpha particles $\frac{m}{q}$ is same and for singly ionized helium $\frac{m}{q}$ is more than alpha particles. So, correct order is $x>y=z$