An `alpha-`particle is accelerated by a potential difference of `10^4 V.` Find the change in its direction of motion, if it enters normally in a region of thickness 0.1 m having transverse magnetic induction of 0.1 tesla. (Given: mass of `alpha-`particle `6.4xx10^(-27)`kg).

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `90^(@)`

Answer

A

Explanation

We have, `V = 10^(4), q = 2e = 2 xx 1.6 xx 10^(-19)C`
d = 0.1 m, B = 0.1 T and `m_(alpha) = 6.4 xx 10^(-27)` kg
Kinetic energy, `K = (1)/(2) m_(alpha) v^(2) = qV = 2eV`
`rArr" "v = sqrt((4eV)/(m_(alpha)))`
`therefore" "R = (m_(alpha)v)/(Bq) = (m_(alpha)v)/(2eB)`
Also, `sin theta = (d)/(R) = (d)/(m_(alpha)v//B.2e) = (2eBd)/(m_(alpha)v)`
`= (2eBd)/(m_(alpha) sqrt((4eV)/(m_(alpha)))) = sqrt((e)/(m_(alpha)V)).Bd`
`= sqrt((1.6 xx 10^(-19))/(6.4 xx 10^(-27)xx 10^(4))) xx 0.1 xx 0.1 = (1)/(2)`
`therefore` Change in direction `theta = 30^(@)`