Question

# Ultraviolet light of wavelength $$2271\;\mathop {\text{A}}\limits^o$$ from a $$100 W$$ mercury source irradiates a photo-cell made of molybdenum metal. If the stopping potential is $$-1.3 V$$, estimate the work function of the metal. How would the photo-cell respond to a high-intensity$$\left( { \sim {{10}^5}\;{\text{W}}{{\text{m}}^{{\text{ - 2}}}}} \right)$$ red light of wavelength $$6328\;\mathop {\text{A}}\limits^0$$ produced by a He-Ne laser? $$\left( {h = 6.63 \times {{10}^{ - 34}}{\text{js,}}\;c = 3 \times {{10}^8}\;{\text{m/s}}} \right)$$

Solution

## Given:The wavelength of the light is $$2271\overset{o}A$$The power of the laser is $$100\ W$$.Stopping potential is $$-1.3\ V$$.The energy required for the emission is:$$W=\dfrac{hc}{\lambda}-eV_o$$$$W=\dfrac{6.6\times10^{-34}\times3 \times10^8}{2271\times10^{-10}}-1.6\times10^{-19}\times1.3$$$$W=6.64\times10^{-19}\ J$$$$W=4.15 eV$$The threshold frequency can be obtained as:$$\nu_o=\dfrac Wh$$$$\nu_o=\dfrac{6.64\times10^{-19}}{6.6\times10{-34}}$$$$=1.006\times10^{15}Hz$$The frequency of the red light is about $$4.74\times10^{14} Hz$$Since the frequency of the incident light required is more than that of the red light, the photocell would respond to the incident light.PhysicsNCERTStandard XII

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