BridgeModern PhysicsFree

The Star-Tracker Test Bench

Photoelectric effect and photon momentum

An engineer at a satellite workshop in Māhia is testing a light sensor for a small satellite. The sensor contains a potassium-coated photocathode with work function

\phi = 2.30\ \text{eV}

. During a bench test it is illuminated by a violet laser diode of wavelength

\lambda = 405\ \text{nm}

delivering a beam power

P = 5.0\ \text{mW}

, all of which strikes the photocathode.

Data: h = 6.63 × 10⁻³⁴ J s · c = 3.00 × 10⁸ m s⁻¹ · e = 1.60 × 10⁻¹⁹ C

(a)

show that2 marks

Show that the energy of one photon from the laser is approximately

3.1\ \text{eV}

(b)

calculate2 marks

Calculate the maximum kinetic energy of the emitted photoelectrons, in eV, and hence the stopping potential that would be needed to reduce the photocurrent to zero. Explain why most photoelectrons leave the photocathode with less than this maximum kinetic energy.

(c)

calculate2 marks

Calculate (i) the momentum of one photon and (ii) the number of photons striking the photocathode each second. Hence (iii) show that the force exerted on the photocathode by the beam, if all photons are absorbed, is about

1.7 \times 10^{-11}\ \text{N}

(d)

explain2 marks

The engineer doubles the laser power, then separately replaces the laser with a red one (

\lambda = 700\ \text{nm}

) of the same power. Explain what happens to the stopping potential and to the photocurrent in each case.

Your score: 0 / 8(0 of 4 parts marked — open “Mark it” on each part)