Question

Please help with this multiple choice physics question.

A metal cylinder is located in a uniform magnetic field. The work function of the metal is Φ.

Photons having an energy of 2Φ strike the side of the cylinder, liberating photoelectrons which travel perpendicular to the magnetic field in a circular path. The maximum radius of the path is r.

If the photon energy is doubled, what will the maximum radius of the path become?

(A) 2r
(B) 3r
(C) r√2
(D) r√3

Answer 1

(D) r√3

Step-by-step explanation:

You want to know how the radius of the path of a photoelectron changes from r if the energy of a photon liberating the electron changes from Φ to 2Φ. The work function of the metal being bombarded is Φ.

Photoelectron energy

The energy of the liberated photoelectrons is the difference between the photon energy and the work function of the surface:

2Φ -Φ = Φ . . . . . gives rise to a path with radius r

When the energy of the photons is doubled, the difference becomes ...

2(2Φ) -Φ = 3Φ . . . . . a factor of 3 times the original electron energy

Radius

The radius of curvature of the electron's path in the uniform perpendicular magnetic field is proportional to the velocity of the electron. In turn, the velocity is proportional to the square root of the energy.

When the energy is multiplied by 3, the radius of the liberated electron's path is multiplied by √3. It becomes r√3.