# Cyclotron Frequency and magnetic field problem

• stunt022
In summary, the conversation is about calculating the cyclotron frequency for various ions in a 3.55 T magnetic field. The atomic masses of the ions are given and the formula used to calculate the frequency is shared. The person has already attempted the calculations and is seeking help as their answers do not match with the online application.

#### stunt022

hey this is my first post, need help with a homework problem.

What is the cyclotron frequency in a 3.55 T magnetic field of the ions listed below? The masses of the atoms are shown in the table. The accuracy of your answers should reflect the accuracy of the data given below. (Although N2+ and CO+ both have a nominal molecular mass of 28, they are easily distinguished by virtue of their different cyclotron resonance frequencies.)

Atomic masses
12C 12.0000 u
14N 14.0031 u
16O 15.9949 u

(a) N2+ in MHz?
(b) O2+ in MHz?
(c) CO+ in MHz?
(numbers are subscript)

i used the following formula to try and get the answer

so i plugged in the numbers and got an equation that looked like this:
f = [[(3.55)*(1.6022*10^-19)]/[2*pi*((2*14.0031)*(1.66053886*10^-27))]]*10^-6
which gave me 1.946533MHz, and is wrong...
i used a charge of a proton(1.6022*10^-19) for q, for m i multiplied the atomic mass by 2 because there are 2 of them, and converted the amu into kilograms after that. finally i converted to MHz from Hz.

the only thing that might not seem right to me is the charge because of how the problem is described but i don't know what that would be.

for (b) O2+ i got 1.704137 MHz
for (c) CO+ i got 1.9473 MHz
which were wrong too.
any help on this i would appreciate.

Are you submitting your homework online?

yes. it tells me imediatly if i am right or wrong

stunt022 said:
yes. it tells me immediately if i am right or wrong
I can see nothing wrong with your working, and my answer agrees with yours (for part (a)). Perhaps, the online application disagrees with your number of significant figures?

## 1. What is the cyclotron frequency and how is it related to magnetic fields?

The cyclotron frequency is the frequency at which a charged particle rotates in a circular motion in a uniform magnetic field. It is directly proportional to the strength of the magnetic field, with a higher magnetic field resulting in a higher cyclotron frequency.

## 2. How is the cyclotron frequency calculated?

The cyclotron frequency can be calculated using the formula f = qB/2πm, where q is the charge of the particle, B is the strength of the magnetic field, and m is the mass of the particle.

## 3. What is the significance of the cyclotron frequency in particle accelerators?

The cyclotron frequency plays a crucial role in particle accelerators, as it determines the rate at which particles can be accelerated. By adjusting the strength of the magnetic field, scientists can control the cyclotron frequency and accelerate particles to the desired energy level.

## 4. How does the cyclotron frequency affect the trajectory of a charged particle?

The cyclotron frequency affects the trajectory of a charged particle by causing it to move in a circular path perpendicular to the magnetic field. The higher the frequency, the tighter the circle and the faster the particle moves.

## 5. Can the cyclotron frequency be used to identify particles?

Yes, the cyclotron frequency can be used to identify particles by measuring the frequency at which they rotate in a magnetic field. Each type of particle has a unique cyclotron frequency, allowing scientists to identify and study different particles in a particle accelerator.

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