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