H2 Physics 19 - Quantum Physics: Photoelectric Effect Calculation

Step 1 - State the problem

Ultraviolet light of wavelength two hundred and fifty nanometres strikes a metal surface with a work function of three point five electron-volts.

Step 1 - State the problem

We want to find the energy of each photon, check whether photoelectric emission occurs, and find the maximum kinetic energy of the emitted electrons.

Step 2 - Calculate the photon energy

The energy of a photon is E equals h f, which can also be written as h c over lambda.

Step 2 - Calculate the photon energy

Substituting: E equals six point six three times ten to the minus thirty-four times three point zero zero times ten to the eight, divided by two point five zero times ten to the minus seven.

Step 2 - Calculate the photon energy

The numerator is one point nine eight nine times ten to the minus twenty-five.

Step 3 - Convert to electron-volts and check threshold

Dividing gives E equals seven point nine six times ten to the minus nineteen joules.

Step 3 - Convert to electron-volts and check threshold

Converting to electron-volts: divide by one point six zero times ten to the minus nineteen to get approximately four point nine seven electron-volts.

Step 3 - Convert to electron-volts and check threshold

Since four point nine seven e V is greater than the work function of three point five e V, photoelectric emission does occur.

Step 4 - Apply Einstein's photoelectric equation

Einstein's photoelectric equation says the photon energy equals the work function plus the maximum kinetic energy of the emitted electron.

Step 4 - Apply Einstein's photoelectric equation

Rearranging: K E max equals E minus phi equals four point nine seven minus three point five, which gives one point four seven electron-volts.

Step 4 - Apply Einstein's photoelectric equation

Converting to joules: one point four seven times one point six zero times ten to the minus nineteen gives two point three five times ten to the minus nineteen joules.

Step 5 - Find the stopping potential

The stopping potential V s is the voltage needed to just stop the fastest photoelectrons.

Step 5 - Find the stopping potential

The work done by the electric field equals the maximum kinetic energy: e V s equals K E max.

Step 5 - Find the stopping potential

So V s equals K E max divided by e, which in electron-volts is simply one point four seven volts.

Step 5 - Find the stopping potential

Key point: increasing the intensity of the light increases the number of photoelectrons but does not change the maximum kinetic energy. Only increasing the frequency increases K E max.