Q.30 Draw a neat schematic diagram of a photo cell.
The photoelectric work function for a metal is 4.2 eV. Find threshold wavelength.
Best answer
Answer: \(\lambda_0\approx2.96\times10^{-7}\) m \(\approx2960\) Å
Schematic diagram of a photocell: [Figure: an evacuated glass (or quartz) bulb containing a semicylindrical metal cathode C coated with a photosensitive material and a thin straight wire anode A along its axis. Light falls on the cathode. The anode is connected to the positive terminal of a battery through a microammeter (\(\mu\)A) and the cathode to its negative terminal.]
When light of frequency above the threshold falls on the cathode, photoelectrons are emitted and are collected by the positive anode, so a photocurrent flows in the circuit and is shown by the microammeter. The current is proportional to the intensity of the light.
Numerical: \(\phi_0=4.2\) eV \(=4.2\times1.6\times10^{-19}=6.72\times10^{-19}\) J.
\(\phi_0=\dfrac{hc}{\lambda_0}\Rightarrow\lambda_0=\dfrac{hc}{\phi_0}=\dfrac{6.63\times10^{-34}\times3\times10^8}{6.72\times10^{-19}}=\dfrac{19.89\times10^{-26}}{6.72\times10^{-19}}\)
\(\lambda_0=2.96\times10^{-7}\) m \(\approx2960\) Å.
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