Question

A mass spectrometer is to be used to separate protons from deuterium nuclei. A deuterium nucleus has the same charge and twice the mass as a proton, since it contains an extra neutron. Both the deuterium and the proton nuclei are accelerated by the same voltage. Which of the following statements is true?

Answers:
The deuterium will not be deflected in the mass spectrometer, since it contains a neutron.
Both the proton and the deuterium will move along the same circular path.
The deuterium will have a larger radius of curvature, since it is more massive.
Mass spectrometers cannot be used to analyze nuclei, only molecular ions.
The deuterium will have a smaller radius of curvature, since it is more massive.

Answer 1

The deuterium will have a larger radius of curvature, since it is more massive.

Step-by-step explanation:

Suppose that the initial velocity of deuterium and protons is the same. According to the relation for centripetal acceleration:

`F = (mv^2)/(r)`

The force is the same due to same electric charge between proton and deuterium. Solving for r:

`r = (mv^2)/(F)`

It means that, the more the mass, the larger the radius due to the directly proportional relation.