Two streams of photons,possessing energies eq | vedclass

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Question

(C) According to Einstein's photoelectric equation,the maximum kinetic energy is given by $KE_{\max} = h
u - \phi$,where $\phi$ is the work function.

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(C) According to Einstein's photoelectric equation,the maximum kinetic energy is given by $KE_{\max} = h
u - \phi$,where $\phi$ is the work function.Since $KE_{\max} = \frac{1}{2}mv^2$,we have $v = \sqrt{\frac{2(h
u - \phi)}{m}}$.For the first case,$h
u_1 = 2\phi$. Thus,$v_1 = \sqrt{\frac{2(2\phi - \phi)}{m}} = \sqrt{\frac{2\phi}{m}}$.For the second case,$h
u_2 = 10\phi$. Thus,$v_2 = \sqrt{\frac{2(10\phi - \phi)}{m}} = \sqrt{\frac{18\phi}{m}}$.The ratio of the maximum velocities is $\frac{v_1}{v_2} = \sqrt{\frac{2\phi}{18\phi}} = \sqrt{\frac{1}{9}} = \frac{1}{3}$.Given the ratio is $x:y = 1:3$,the value of $x$ is $1$.

Two streams of photons,possessing energies equal to twice and ten times the work function of a metal,are incident on the metal surface successively. The ratio of the maximum velocities of the photoelectrons emitted in the two respective cases is $x:y$. The value of $x$ is ...... .

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