Chapter 32, Problem 3P

To determine

The frequency of applied voltage in cyclotron for alpha particles.

Answer to Problem 3P

Solution:

The frequency of the applied voltage is $13.5\times {10}^7\text{Hz}$

Explanation of Solution

Given info:

Form the Example 32-2 the magnetic field is 1.7T and Radius of cyclotron is R=0.25.

Formula used:

The equation to determine the frequency is given by

$f=\frac{qB}{2\pi m}$……………………………..I

Calculation:

Now alpha particles have 2 protons and 2 neutrons hence the charge on alpha particles is twice that of a proton.

Thus, $q=\text{2}\times \text{1}.\text{6x1}{0}^{-\text{19}}\text{kg}=\text{3}.\text{2}\times \text{1}{0}^{-\text{19}}\text{C}$

And the mass, $m=\text{4}\times \text{1}.\text{67}\times \text{1}{0}^{-\text{19}}\text{kg }=\text{6}.\text{68}\times \text{1}{0}^{-\text{19}}\text{C}$

Substituting the values in equation I we get.

$f=\frac{2\times 1.6\times {10}^{-19}\times 1.7}{2\times 3.14\times 4\times 1.67\times {10}^{-19}}$

$f=13.5\times {10}^7\text{Hz}$