Question 160: Dual Nature of Matter and Radiation

Question

When radiation of wavelength $$\lambda$$ is incident on a metallic surface, the stopping potential of ejected photoelectrons is 4.8 V. If the same surface is illuminated by radiation of double the previous wavelength, then the stopping potential becomes 1.6 V. The threshold wavelength of the metal is :

Accepted Answer

$${V_s} = hv - \phi $$
$$4.8 = {{hc} \over \lambda } - \phi $$ ..... (i)
$$1.6 = {{hc} \over {2\lambda }} - \phi $$ ..... (ii)
Using above equation (i) - (ii)
$$3.2 = {{hc} \over \lambda } - {{hc} \over {2\lambda }}$$
$$3.2 = {{hc} \over {2\lambda }}$$ ..... (iii)
$$\left[ {\lambda  = {{hc} \over {6.4}}} ight]$$
Put in equation (ii)
$$\phi$$ = 1.6
$${{hc} \over {{\lambda _{th}}}} = 1.6$$
$${\lambda _{th}} = {{hc} \over {1.6}}$$
$$ = \left( {{{hc} \over {6.4}}} ight) 	imes 4 = 4\lambda $$

Answer

2$$\lambda$$

Answer

4$$\lambda$$

Answer

8$$\lambda$$

Answer

6$$\lambda$$

Dual Nature of Matter and Radiation

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