22.2 Photoelectric Effect

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2. Photons — A Quick Reminder

Light travels as packets of energy called photons. The energy of a single photon depends on the frequency of the light:

$E = hf$

Or, since frequency and wavelength are related by $c = f\lambda$:

$E = \frac{hc}{\lambda}$

Where:

• $E$ = energy of one photon (in Joules, J)
• $h$ = Planck's constant = $6.63 \times 10^{-34}$ J s
• $f$ = frequency of the radiation (in Hz)
• $c$ = speed of light = $3 \times 10^8$ m/s
• $\lambda$ = wavelength (in metres)

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Threshold Wavelength (λ₀)

Threshold wavelength is the maximum wavelength of electromagnetic radiation that can cause photoelectric emission.

• Because a longer wavelength means a lower frequency (and therefore less energy per photon), there is a maximum wavelength above which no emission occurs.
• The relationship between threshold frequency and threshold wavelength comes from the wave equation:

$c = f_0 \lambda_0 \implies \lambda_0 = \frac{c}{f_0}$

Why do different metals have different threshold frequencies?

Each metal holds its electrons with a different strength. Metals that hold electrons loosely (like sodium and potassium — called alkali metals) have low threshold frequencies, so even visible light can cause emission. Metals that hold electrons tightly (like iron and copper — transition metals) have high threshold frequencies, so you need ultraviolet light to cause emission.