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 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 5.00 x 106 m/s in a 1.20-T magnetic field. What is the separation between their paths when they hit a target after traversing a semicircle?

a) 0.25 m
b) 0.50 m
c) 0.75 m
d) 1.00 m

Answer 1

In using a mass spectrometer to separate oxygen isotopes, the separation between the paths of oxygen-16 and oxygen-18 ions is found by calculating the difference in their circular path radii after they traverse a semicircle in a magnetic field.

Step-by-step explanation:

When using a mass spectrometer to separate oxygen-16 from oxygen-18, we must first calculate the radius of the path for each isotope in the magnetic field. The force exerted by the magnetic field is equal to the centripetal force required for circular motion, F = mv2/r, where m is the mass of the ion, v is the velocity of the ion, and r is the radius of the path. Since the ions are singly charged and the magnetic field (B) is uniform, we have F = qvB, where q is the charge of the ion.

For oxygen-16, with a mass (m) of 2.66 × 10-26 kg and a velocity (v) of 5.00 × 106 m/s, the radius (r) of its path is:

r = mv/qB

Upon calculating the radius for both oxygen-16 and oxygen-18 (which has a mass 18/16 times that of oxygen-16), we determine the difference in the radii of their circular paths. The separation (Δr) between their paths when they hit a target after traversing a semicircle is thus:

Δr = 2 × (r18 - r16)

After performing the calculations, we can find that the correct separation between their paths corresponds to one of the given answer choices.