a cyclotron is operated at an oscillator frequency of 12 mhz and has radius of 53cm a what is th

Step 1: Calculate the magnetic field strength using the formula ( B = frac{q cdot v}{r} ), w

A cyclotron is operated at an oscillator frequency of 12 mhz...

A cyclotron is operated at an oscillator frequency of 12 MHz and has a radius of 53 cm. a) What is the magnitude of the magnetic field needed for deuterons to be accelerated in the cyclotron? b) What is the resulting kinetic energy of the deuterons?

Transcript

00:01 When the charge ultrek moves in a region of magnetic field, it follows a circular path, which rate with the specific radius.

00:08 We can solve for the magnetic field strength using the following formula, where n is the mass, b is the speed, q is the charge, and r is the regions of that.

00:18 B is the magnetic field strength expressed in tesla.

00:21 In this problem, we are given with a cyclotron that is operated with an oscillator frequency of 12 megahertz, and as a radius of 53 centimeters.

00:30 We want to find the magnitude of the magnetic field needed for deuterons be accelerated in the said cyclotone as well as the kinetic energy of the jeterons.

00:43 Now, jeteron is a proton with a mass of twice the mass of proton.

00:48 Its charge is equal to the charge of proton, which is 1 .609 times 10 to the negative 19 .000.

00:54 As the mass of one proton is 1 .673 times 10 to the power of negative 27.

01:01 Thus, the mass of deuterol would be twice of these.

01:04 So we will have it as 3 .35 times 10 to the negative 27.

01:18 So first is that we will find you b, the magnetic field straight, using the formula that we use here.

01:27 So we note that the frequency of oscillation can also be expressed in terms of the speed as follows.

01:34 Over 2 .5r.

01:37 This is this formula suggests that we have to divide the speed of the speed of the charged particle divided by the distance.

01:49 So that distance is the circumference of the circle with a specific radius of r...

Question

A cyclotron is operated at an oscillator frequency of 12 MHz and has a radius of 53 cm. a) What is the magnitude of the magnetic field needed for deuterons to be accelerated in the cyclotron? b) What is the resulting kinetic energy of the deuterons?

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