Question

A stream of protons and deuterons in a vacuum chamber enters a uniform magnetic field. Both protons and deuterons have been subjected to same accelerating potential, hence the kinetic energies of the particles are the same. if the ion-stream is perpendicular to the magnetic field and the protons move in a circular path of radius 15 cm, find the radius of the path traversed by the deuterons. Given that mass of deuteron is twice that of a proton.

Answer 1

$r=\frac{mV}{qB}$, V$=\sqrt{2mk}=\frac{1}{2}m{v}^2=q{V}_{p}qK=q{V}_{p}q=\sqrt{2mq{V}_{pot}}$

$=\frac{m\sqrt{2mq{V}_{pot}}}{qB}$

$=()\frac{m^{\frac{3}{2}}}{q}$
$\frac{r_p}{r_d}$ $=\frac{m_p^{\frac{3}{2}}}{q_p}\times \frac{q_d}{m{{}_d}^{\frac{3}{2}}}$
$=({\frac{m_p}{m_d})}^{\frac{3}{2}}\frac{q_q}{q_p}\to 1$
$=(\frac{1}{2}{)}^{\frac{3}{2}}$