# Photoelectric Effect

### Gold Leaf Electroscope Experiment

The gold leaf electroscope experiment proves that light has particle-like properties. It involves the device shown below: two thin strips of gold leaf connected to a negatively charged metal plate. Since the two gold strips will be both negatively charged, they will repel each other, and a non-fixed gold leaf will rise up. The result from shining visible and ultraviolet light on the metal plate proves that light is not simply a wave, and proves the photoelectric effect.

Using the theory of light being a wave, we can expect that shining light of any wavelength onto the metal plate would cause the gold leaf to fall. However, this is not what happens - the gold leaf does not fall under even the brightest visible light sources. Electrons were only released from the electronscope when high-frequency light was used, e.g. ultraviolet light.

#### Explanation

This phenomenon can be explained by the following:

1. The energy of an electromagnetic wave is directly proportional to its frequency.
2. Electromagnetic waves travel in discrete "packets", called photons.
3. Metals have a minimum energy threshold required per discrete photon to release electrons.

This minimum energy threshold is known as the work function.

Confusing names!

Despite its name, a work function is not a function - it is a property of metals, similar to atomic number or atomic mass for example.

### Formulae

#### Energy of a Photon Formula

$E=hf$
Variable Key

• $E$ is the energy of a photon, in joules.
• $h$ is the Planck constant, approximately .
• $f$ is the frequency of the wave, in hertz.

#### Photoelectric Effect Formula

${E}_{k}=hf-h{f}_{o}$
Variable Key

• ${E}_{k}$ is the kinetic energy of the released photoelectron.
• $hf$ is the energy of a photon (from the above formula), in joules.
• $h$ is the Planck constant.
• $f$ is the frequency of the photon, in hertz.
• $h{f}_{o}$ is the work function.
• $h$ is the Planck constant.
• ${f}_{o}$ is the threshold frequency, in hertz.