Question

A mass spectrometer is being used to separate common oxygen-16 from the much rarer oxygen-18, taken from a sample of old glacial ice. (The relative abundance of these oxygen isotopes is related to climatic temperature at the time the ice was deposited.) The ratio of the masses of these two ions is 16 to 18, the mass of oxygen-16 is 2.66 ✕ 10⁻²⁶ kg, and they are singly charged and travel at 3.70 ✕ 10⁶ m/s in a 1.70 T magnetic field. What is the separation (in m) between their paths when they hit a target after traversing a semicircle?

Answer 1

Using Force balance on charged particle in mass spectrometer is given by:

Fc = Fm

m*V^2/R = q*V*B

R = m*V/(q*B)

Now distance traveled by Oxygen-16 in semicircle will be:

d1 = 2*R1 = 2*m1*V/(q*B)

m1 = mass of O-16 = 2.66*10^-26 kg

V = Speed of charged particle = 3.70*10^6 m/sec

q = charged particle = 1.6*10^-19 C

B = Magnetic field = 1.70 T

So,

r1 = 2.66*10^-26*3.70*10^6/(1.6*10^-19*1.70)

r1 = 0.361838 m

Now distance traveled by Oxygen-18 in semicircle will be:

d2 = 2*R2 = 2*m2*V/(q*B)

m2 = mass of O-18

given that m1/m2 = 16/18

m2 = m1*(18/16) = 2.66*10^-26*(18/16) = 2.9925*10^-26 kg

V = Speed of charged particle = 3.70*10^6 m/sec

q = charged particle = 1.6*10^-19 C

B = Magnetic field = 1.70 T

So,

r2 = 2.9925*10^-26*3.70*10^6/(1.6*10^-19*1.70)

r2 = 0.407068 m

So, Separation between their paths will be:

d = d2 - d1 = 2*(r2 - r1)

d = 2*(0.407068 - 0.361838) = 0.0905 m

d = 0.0905 m = 9.05*10^-2 m