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Dual Nature of Matter question bank (Physics)

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Q1.

An experimental study of the photoelectric effect involves a metal of work function $\phi_0$. What is the smallest wavelength of the incident photon to photoemit an electron of mass $m$ which has the same de Broglie wavelength as that of the incident photon? [Given $h$ is the Planck's constant, $c$ is the speed of light, and $\phi_0 \ll mc^2$]

(A)

$\dfrac{h}{mc}\left(1 - \sqrt{1 - \dfrac{2\phi_0}{mc^2}}\right)^{-1}$

(B)

$\dfrac{h}{mc}\left(1 + \sqrt{1 - \dfrac{2\phi_0}{mc^2}}\right)^{-1}$

(C)

$\dfrac{h}{mc}\left(1 - \sqrt{1 - \dfrac{\phi_0}{mc^2}}\right)^{-1}$

(D)

$\dfrac{h}{mc}\left(1 + \sqrt{1 - \dfrac{\phi_0}{mc^2}}\right)^{-1}$

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Q2.

Consider normal incidence of a monochromatic beam of photons of power $P$ on a flat surface. Of the incident beam, 10% gets absorbed, 10% gets transmitted, and the rest is reflected by the flat surface. If $c$ is the speed of light, what is the force exerted on the flat surface by the beam?

(A)

$1.8\dfrac{P}{c}$

(B)

$0.9\dfrac{P}{c}$

(C)

$1.6\dfrac{P}{c}$

(D)

$1.7\dfrac{P}{c}$

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