AcademyPhotons
Academy
Photoelectric Effect
Level 1 - Physics topic page in Photons.
Principle
The photoelectric effect shows that light transfers energy in packets called photons. A metal emits electrons only when one photon has enough energy to overcome the work function.
Increasing intensity increases the number of photons, not the energy of each photon.
Notation
\(E_\gamma\)
photon energy
\(\mathrm{J,\;eV}\)
\(h\)
Planck constant
\(\mathrm{J\,s}\)
\(f\)
frequency
\(\mathrm{s^{-1}}\)
\(\lambda\)
wavelength
\(\mathrm{m}\)
\(\phi\)
work function
\(\mathrm{J,\;eV}\)
\(K_{\max}\)
maximum photoelectron kinetic energy
\(\mathrm{J,\;eV}\)
\(V_s\)
stopping potential
\(\mathrm{V}\)
Method
Derivation 1: Photon energy
Each photon has energy set by frequency. Using \(c=f\lambda\), photon energy can also be written in terms of wavelength.
Frequency form
\[E_\gamma=hf\]
Wavelength form
\[E_\gamma=\frac{hc}{\lambda}\]
Derivation 2: Energy balance at the surface
One photon gives its energy to one electron. The work function is the minimum energy needed to escape.
Photoelectric equation
\[K_{\max}=hf-\phi\]
Stopping potential
\[eV_s=K_{\max}\]
Derivation 3: Threshold condition
At threshold, emitted electrons have zero maximum kinetic energy.
Threshold frequency
\[f_0=\frac{\phi}{h}\]
Threshold wavelength
\[\lambda_0=\frac{hc}{\phi}\]
Rules
Photon energy
\[E_\gamma=hf=\frac{hc}{\lambda}\]
Photoelectric equation
\[K_{\max}=hf-\phi\]
Stopping potential
\[eV_s=K_{\max}\]
Threshold frequency
\[f_0=\frac{\phi}{h}\]
Threshold wavelength
\[\lambda_0=\frac{hc}{\phi}\]
Examples
Question
Light of wavelength
\[280\,\mathrm{nm}\]
strikes a metal with work function \[2.20\,\mathrm{eV}\]
Find the photon energy using \[hc=1240\,\mathrm{eV\,nm}\]
Answer
\[E_\gamma=\frac{1240}{280}=4.43\,\mathrm{eV}\]
Checks
- No electrons are emitted if the photon energy is below the work function.
- A larger frequency gives larger electron kinetic energy.
- A larger intensity above threshold gives more emitted electrons.
- The stopping potential measures maximum kinetic energy per unit charge.