Question 5: Dual Nature of Matter and Radiation

Question

The de-Broglie wavelength of an electron moving with a velocity $$\frac{c}{3}$$ (c = 3 $$	imes$$ 108 m/s) is equal to the wavelength of photon. The ratio of the kinetic energies of electron and photon is

Accepted Answer

The de-Broglie wavelength, $$\lambda  = {h \over {mv}}$$
Here, $${\lambda _e} = {h \over {{m_e}{e \over 3}}}$$ and $${\lambda _p} = {h \over {{m_p}c}}$$
Given, $${\lambda _e} = {\lambda _p}$$
So, $${h \over {{m_e}{c \over 3}}} = {h \over {{m_p}c}}$$
$$ \Rightarrow {{{m_e}} \over {{m_p}}} = 3$$
Ratio of $$KE = {{{K_e}} \over {{K_p}}} = {{{1 \over 2}{m_e}v_e^2} \over {{1 \over 2}{m_p}v_p^2}} = {1 \over 3}$$
($$\because$$ $${{{m_e}} \over {{m_p}}} = 3,\,{v_e} = {c \over 3}$$ and $${v_p} = c$$)

Answer

1 : 4

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1 : 3

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1 : 2

Answer

2 : 1

Dual Nature of Matter and Radiation

The de-Broglie wavelength of an electron moving with a velocity $\frac{c}{3} (c = 3 \times$ 108 m/s) is equal to the wavelength of photon. The ratio of the kinetic energies of electron and photon is

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