The Photoelectric Equation | CAIE 9702 Paper 4 Notes

Chapters

Paper 4

Physics9702

Work function is the minimum escape energy

Definition

2 marks

What is meant by the work function energy of a metal?

Model answer: The work function is the minimum energy required to remove an electron from the surface of the metal.

The word minimum and the phrase from the surface are both important (9702/41/O/N/22 Q8(a)).

hf=\Phi+E_{\max}

Symbols

$h$ = Planck constant (J s)
$f$ = frequency of the incident radiation (Hz)
$\Phi$ = work function of the metal (J)
$E_{\max}$ = maximum kinetic energy of an emitted electron (J)

The fastest photoelectrons come from electrons that require only the minimum escape energy. Other emitted electrons may leave with less kinetic energy.

Key idea

Einstein's equation gives the maximum kinetic energy, not the kinetic energy of every emitted electron. All energy terms must use the same unit; convert the kinetic energy to joules before using it to calculate a speed.

If the maximum electron speed is given, calculate its kinetic energy from the electron mass and speed.

E_{\max}=\dfrac{1}{2}m v_{\max}^{2}

Symbols

$E_{\max}$ = maximum kinetic energy of an emitted electron (J)
$m$ = mass of an electron (kg)
$v_{\max}$ = maximum speed of an emitted electron (m s⁻¹)

Worked example

Use Einstein's equation above the threshold

Radiation of frequency 9.0 × 10¹⁴ Hz reaches a metal with work function 2.10 eV. Calculate the maximum electron speed.

Convert the work function to joules.
$\Phi=2.10\ \mathrm{eV}$
$\Phi=3.36\times10^{-19}\ \mathrm{J}$
Subtract the work function from the energy of one photon.
$hf=5.97\times10^{-19}\ \mathrm{J}$
$E_{\max}=hf-\Phi$
$E_{\max}=2.61\times10^{-19}\ \mathrm{J}$
Use the maximum kinetic energy to find the maximum speed.
$v_{\max}^2=\dfrac{2E_{\max}}{m}$
$v_{\max}^2=5.73\times10^{11}\ \mathrm{m^2\,s^{-2}}$
$v_{\max}=7.6\times10^5\ \mathrm{m\,s^{-1}}$

Answer

v_{\max}=7.6\times10^5\ \mathrm{m\,s^{-1}}

Your turncalculation check

A photon has energy 5.0 eV and the metal work function is 2.0 eV. What is the maximum photoelectron kinetic energy?

Show worked answer

Subtract the minimum escape energy from the photon energy. The maximum kinetic energy is 3.0 eV.

Work function is the minimum escape energy

Definition

2 marks

What is meant by the work function energy of a metal?

Model answer: The work function is the minimum energy required to remove an electron from the surface of the metal.

The word minimum and the phrase from the surface are both important (9702/41/O/N/22 Q8(a)).

hf=\Phi+E_{\max}

Symbols

$h$ = Planck constant (J s)
$f$ = frequency of the incident radiation (Hz)
$\Phi$ = work function of the metal (J)
$E_{\max}$ = maximum kinetic energy of an emitted electron (J)

The fastest photoelectrons come from electrons that require only the minimum escape energy. Other emitted electrons may leave with less kinetic energy.

Key idea

If the maximum electron speed is given, calculate its kinetic energy from the electron mass and speed.

E_{\max}=\dfrac{1}{2}m v_{\max}^{2}

Symbols

$E_{\max}$ = maximum kinetic energy of an emitted electron (J)
$m$ = mass of an electron (kg)
$v_{\max}$ = maximum speed of an emitted electron (m s⁻¹)

Worked example

Use Einstein's equation above the threshold

Radiation of frequency 9.0 × 10¹⁴ Hz reaches a metal with work function 2.10 eV. Calculate the maximum electron speed.

Convert the work function to joules.
$\Phi=2.10\ \mathrm{eV}$
$\Phi=3.36\times10^{-19}\ \mathrm{J}$
Subtract the work function from the energy of one photon.
$hf=5.97\times10^{-19}\ \mathrm{J}$
$E_{\max}=hf-\Phi$
$E_{\max}=2.61\times10^{-19}\ \mathrm{J}$
Use the maximum kinetic energy to find the maximum speed.
$v_{\max}^2=\dfrac{2E_{\max}}{m}$
$v_{\max}^2=5.73\times10^{11}\ \mathrm{m^2\,s^{-2}}$
$v_{\max}=7.6\times10^5\ \mathrm{m\,s^{-1}}$

Answer

v_{\max}=7.6\times10^5\ \mathrm{m\,s^{-1}}

Your turncalculation check

A photon has energy 5.0 eV and the metal work function is 2.0 eV. What is the maximum photoelectron kinetic energy?

Show worked answer

Subtract the minimum escape energy from the photon energy. The maximum kinetic energy is 3.0 eV.