Question

A cyclotron is used to accelerate proton to a kinetic energy of 5mev.if the strngth of magnetic filed in the cylotron is 2t find2T find radius n frequency needed for the applied alternating voltage of the cyclotron

Answer 1

The radius and frequency are 11.88 x 10⁻⁸ m and f = 5.6 x 10¹⁰ Hz respectively

Explanation :

we know that

mass of electron, m = 9.1 x 10⁻³¹ kg

charge of electron, e = 1.6 x 10⁻¹⁹

Given kinetic energy,

E = 5 x 10⁻³ eV = 5 x 10⁻³ x 1.6 x 10⁻¹⁹ = 8 x 10⁻²² J

=> 1/2 x mv² = 8 x 10⁻²²

=> v² = 8 x 10⁻²² x 2/(9.1 x 10⁻³¹) = 17.5 x 10⁸

=> v = 4.18 x 10⁴ m/s

The radius of the circle in which the particle move is given by,

R = mv/eB

=> R = (9.1 x 10⁻³¹ x 4.18 x 10⁴)/(1.6 x 10⁻¹⁹ x 2)

R= 11.88 x 10⁻⁸ m

The frequency of the source is given by,

f = eB/2πm

=> f = (1.6 x 10⁻¹⁹ x 2)/( 2 x 3.14 x 9.1 x 10⁻³¹)

=> f = 5.6 x 10¹⁰ Hz