How Do You Calculate Cyclotron Frequency for Ions in a Magnetic Field?

[boozi]

Homework Statement

What is the cyclotron frequency in a 3.10 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.)

(a) N2+ ______ MHz
(b) O2+ ______ MHz
(c) CO+ ______ MHz


B = 3.10 T
2 Oxygen molecules positively ionized (+1) = 2 * 15.9949 u * 1.661*10^-27 = 5.31*10^-26kg

2 Nitrogen molecules positively ionized (+1) = 2 * 14.0031 u * 1.661*10^-27 =
4.6518*10^-26kg

Carbon monoxide positively ionized (+1) = 12.0000 + 15.9949 u * 1.661*10^-27 =
4.64995*10^-26kg

Homework Equations

frequency = (qB)/(2pi*m)

The Attempt at a Solution

Well, I've calculated the result so many times, and for some reason, it gives me the wrong answer... I'm supposed to end up with MHz, so what I've done was plug in all the "supposedly" correct numbers, which are the following:
q = 1.602*10^-19C
B = 3.10 T
m = The mass of the molecule - the mass of one electron.
Can anyone tell me why I'm wrong? Here are my answers:
N2+ 1.6991 MHz
O2+ 1.4875 MHz
CO+ 1.6998 MHz

Thanks in advance!

 

[anathema]

Hello there,

Your calculations look correct, but I believe the issue may be with the accuracy of the data given. The masses of the atoms are given with a certain number of significant figures, but when you multiply them together, the result may not have the same level of accuracy. For example, the mass of N2+ is given as 4.6518*10^-26 kg, but when you multiply that by q and B, the result may not have the same level of accuracy.

To ensure the accuracy of your answers, you may want to use the full precision of the masses (e.g. 14.003074 u instead of 14.0031 u) and then round your final answers to the appropriate number of significant figures. I hope this helps!

 

[m2003]

First of all, it is important to note that the given masses of the ions are given in atomic mass units (u), which are different from kilograms (kg). Therefore, the first step would be to convert the masses to kilograms before plugging them into the equation.

(a) N2+:
m = 2 * 14.0031 u * 1.661*10^-27 kg/u = 4.6517*10^-26 kg
q = 1.602*10^-19 C
B = 3.10 T
Using the equation, frequency = (qB)/(2pi*m), we get:
frequency = (1.602*10^-19 C * 3.10 T)/(2pi*4.6517*10^-26 kg) = 1.6991 MHz

(b) O2+:
m = 2 * 15.9949 u * 1.661*10^-27 kg/u = 5.3107*10^-26 kg
q = 1.602*10^-19 C
B = 3.10 T
Using the equation, frequency = (qB)/(2pi*m), we get:
frequency = (1.602*10^-19 C * 3.10 T)/(2pi*5.3107*10^-26 kg) = 1.4875 MHz

(c) CO+:
m = 12.0000 u * 1.661*10^-27 kg/u + 15.9949 u * 1.661*10^-27 kg/u = 4.6500*10^-26 kg
q = 1.602*10^-19 C
B = 3.10 T
Using the equation, frequency = (qB)/(2pi*m), we get:
frequency = (1.602*10^-19 C * 3.10 T)/(2pi*4.6500*10^-26 kg) = 1.6998 MHz

Therefore, the correct answers are:
(a) N2+ 1.6991 MHz
(b) O2+ 1.4875 MHz
(c) CO+ 1.6998 MHz

It is possible that the incorrect answers were obtained due to rounding errors or incorrect unit conversions. It is important to double check all calculations and ensure that the units are consistent throughout.