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 2.66e−26kg, and they are singly charged and travel at 5.00×106m/s in a 1.20-T magnetic field. What is the separation between their paths when they hit a target after traversing a semicircle?

Answer 1

Answer: 0.076 m

Explanation:

Magnetic force= centripetal force;

F(B) = F(c) --------------------------(1)

Bqv= mv^2/R---------------------(2)

Where B= magnetic field,q= charge, = mass, R= radius of the circular path.

Radius of the circular path,R= mv/qB.

Mass of oxygen-16 is 2.66e−26kg, and they are singly charged = 18/16(mass ratio= 18:16)

18/16 × (2.26 × 10^ -26 kg)

= 2.99 × 10^26 kg

∆d=2r(18)-2r(16)-----------------(3)

r(18) is the radius of mass of oxygen-18,

r(16) is the radius of mass of oxygen-16.

From the question, v= 3.7×10^6 m/s, q= 1.6×10^-9 C.

From equation (2) above we have;

R= MV/qB------------------------(4)

This equation (4) is used in solving for the distance between the two.

Solving;∆d=2r(18)-2r(16)

∆d = 2[m(18) - m(16)] v/ qB

M(18)-m(16) =(2.99-2.66)× 10^-26:

qB= 1.6×10^-19×2 = 3.2×10^-19

= (2.99-2.66)× 10^-26/ 3.2× 10^-19

= 0.076 m