Question
Derive Einstein’s photoelectric equation $\frac{1}{2}\text{m}\text{v}^2=\text{h}\nu-\text{h}\nu_0.$
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Answer
Einstein’s Explanation of Photoelectric Effect:Einstein’s Photoelectric Equation:
Einstein explained photoelectric effect on the basis of quantum theory. The main points are,
$\text{E}_\text{K}=\text{h}\nu-\text{h}\nu_0$ $\Rightarrow\ \frac{1}{2}\text{mv}^2=\text{h}\nu-\text{h}\nu_0\dots(\text{iii})$This is another form of Einstein's photoelectric equation.
Einstein explained photoelectric effect on the basis of quantum theory. The main points are,
- Light is propagated in the form of bundles of energy. Each bundle of energy is called a quantum or photon and has energy hν where h = Planck’s constant and ν = frequency of light.
- The photoelectric effect is due to collision of a photon of incident light and a bound electron of the metallic cathode.
- When a photon of incident light falls on the metallic surface, it is completely absorbed. Before being absorbed it penetrates through a distance of nearly 10-8m (or $100\mathring{\text{A}}$). The absorbed photon transfers its whole energy to a single electron. The energy of photon goes in two parts: a part of energy is used in releasing the electron from the metal surface (i.e., in overcoming work function) and the remaining part appears in the form of kinetic energy of the same electron.
$\text{E}_\text{K}=\text{h}\nu-\text{h}\nu_0$ $\Rightarrow\ \frac{1}{2}\text{mv}^2=\text{h}\nu-\text{h}\nu_0\dots(\text{iii})$This is another form of Einstein's photoelectric equation.
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