The red edge of the photoelectric effect for a metal corresponds to a wavelength of 500 nm. Find the work function of the electron — Physics problems | PhysLabo
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Work function of an electron

Medium 11 grade Quantum Physics / Photoelectric Effect

The red edge of the photoelectric effect for a metal corresponds to a wavelength of $\lambda = 500$ nm. Find the work function of the electron. Planck's constant is $h = 6.63 \cdot 10^{-34}$ J·s and the speed of light is $c = 3 \cdot 10^8$ m/s.

Given
  • $\lambda = 500$ nm $= 5 \cdot 10^{-7}$ m
  • $h = 6.63 \cdot 10^{-34}$ J·s
  • $c = 3 \cdot 10^8$ m/s
  • $A = ?$
Hints
Hint 1 / 2
At the red edge $E_k = 0$, so $A = hc/\lambda$ — the energy of a photon with that wavelength.
Hint 2 / 2
1 eV = 1.6e-19 J — use this to convert the answer to electronvolts.
Solution

At the red edge the kinetic energy of the photoelectrons is zero, so the work function equals the photon energy:

$$A = \frac{hc}{\lambda} = \frac{6.63 \cdot 10^{-34} \cdot 3 \cdot 10^{8}}{5 \cdot 10^{-7}} \approx 3.98 \cdot 10^{-19} \text{ J}$$

Convert to electronvolts ($1$ eV $= 1.6 \cdot 10^{-19}$ J):

$$A = \frac{3.98 \cdot 10^{-19}}{1.6 \cdot 10^{-19}} \approx 2.49 \text{ eV}$$

Answer

$A \approx 3.98 \cdot 10^{-19}$ J $\approx 2.49$ eV