Question

• Two singly ionized atoms move into a magnetic fields of magnitude 0.100 T pointing into the page. Each has a speed of 1.00 X 106 m/s. The nucleus of the first atom contains one proton and has a mass of 1.67 X 10-27 kg, while the nucleus of the second atom contains a proton and a neutron and has a mass of 3.34 X 10-27 kg. Atoms with the same number of protons in the nucleus but different masses are called isotopes. The two isotopes here are hydrogen and deuterium. Find their distance of separation when they strike a photographic plate.

Answer 1

Given data:

Two singly ionized atoms are moving perpendicular to the Magnetic field. (As the direction of the magnetic field is into the page and the motion of the atoms is on the page)

Magnitude of the magnetic field = 0.1 T

Speed of the ionized atoms = 1.00 x 10⁶ m/s

Mass of proton (ionized hydrogen) = 1.67 x 10^-27 kg

Mass of proton and a neutron ( ionized deuterium) = 3.34 x 10^-27 kg

We know that charged particles moving perpendicular to the magnetic field follow a circular path. Here the Lorentz force will provide the necessary force to balance the centripetal force experienced by the charged particles. Therefore:

Where q is the charge of the particle

v is the velocity of the particle

B is the applied magnetic field

r is the radius of the circular motion of the charged particles

Cancelling v from the both sides and rearranging above equation to get the radius :

Substituting the values for a proton we get:

Similarly substituting the values for the proton and neutron combination we get:

Now distance of separation will be given by:

You can easily see this in the diagram:

Substituting values in above formula we get:

Which is the required answer

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