Question

This is what I did.

I. Suppose that an ion source in a mass spectrometer produces doubly ionized gold ions (Au2+), each with a mass of 3.27 × 10-25 kg The ions are accelerated from rest through a potential difference of 1.40 kV. Then, a 0.440 T magnetic field causes the ions to followa circular path. Determine the radius of the path. x 0.172 m

r = (m*v) / (qB)

To find v, v= sqrt( 2*q*V/m) = 37013.9

and I put this number and the given numbers to find 'r', but I got it wrong. What did I do wrong?

Answer 1

Given, m = 3.27 times 10^- 25 kg, v = 1.4 kv = 1.4 times 10^3 v B = 0.44 T since it is doubly ionized, charge, q = 2 e^bar = 2 times 1.6 times 10^- 19 C q = 3.2 times 10^- 19 C Formula r = mv/Bq and v = squareroot 2 q v/m therefore velocity v = squareroot 2 times 3.2 times 10^- 19 times 1.4 times 10^3/3.27 times 10^25 = 5.234 times 10^4 radius, r mv/Bq therefore r = 3.27 times 10^25 times 5.234 times 10^4/0.44 times 3.2 times 10^- 19 = 12.155 times 10^- 2 (or) r = 0.1215 m