The work function for a certain metal is 4.2 eV. Will this metal … - Vidyadip

Question

The work function for a certain metal is 4.2 eV. Will this metal give photoelectric emission for incident radiation of wavelength 330 nm?

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Answer

No
Work function of the metal, $\phi_\circ=4.2\ \text{eV}$
Charge on an electron, $e = 1.6 \times 10^{-19} C$
Planck's constant,$ h = 6.626 \times 10^{-34} Js$
Wavelength of the incident radiation, $\lambda=330\ \text{nm}=330\times10^{-9}\ \text{m}$
Speed of light, $c = 3 \times 10^8 m/s$
The energy of the incident photon is given as:
$\text{E}=\frac{\text{hc}}{\lambda}$
$=\frac{6.626\times10^{-34}\times3\times10^{8}}{330\times10^{-9}}=6.0\times10^{-19}\ \text{J}$
$=\frac{6.0\times10^{-19}}{1.6\times10^{-19}}=3.76\ \text{eV}$
It can be observed that the energy of the incident radiation is less than the work function of the metal. Hence, no photoelectric emission will take place.

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