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Dual Nature of Radiation and Matter — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsDual Nature of Radiation and Matter3 Marks
Question
The work function for the following metals is given: $Na: 2.75 eV; K: 2.30 eV; Mo: 4.17 eV; Ni: 5.15 eV.$ Which of these metals will not give photoelectric emission for a radiation of wavelength $3300 \mathring A$ from a $He-Cd$ laser placed $1 m$ away from the photocell? What happens if the laser is brought nearer and placed $50 \ cm$ away?
✓

Answer

$Mo$ and $Ni$ will not show photoelectric emission in both cases
Wavelength for a radiation, $\lambda=3300\ \mathring{\text{A}}=3300\times10^{-10}\ \text{m}$
Speed of light, $c = 3 \times 10^8 m/s$
Planck's constant, $h = 6.6 \times 10^{-34} Js$
The energy of incident radiation is given as:
$\text{E}=\frac{\text{hc}}{\lambda}$
$=\frac{6.6\times10^{-34}\times3\times10^{8}}{3300\times10^{-10}}=6\times10^{-19}\ \text{J}$
$\frac{6\times10^{-19}}{1.6\times10^{-19}}=3.158\ \text{eV}$
It can be observed that the energy of the incident radiation is greater than the work function of $Na$ and $K$ only.
It is less for $Mo$ and $Ni.$
Hence, $Mo$ and $Ni$ will not show photoelectric emission.
If the source of light is brought near the photocells and placed $50 \ cm$ away from them,
then the intensity of radiation will increase. This does not affect the energy of the radfation.
Hence, the result will be the same as before.
However, the photoelectrons emitted from $Na$ and $K$ will increase in proportion to intensity.

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