First slide

Matter waves (DC Broglie waves)

Question

An electron of mass $m$ and a photon have same energy $E$ . The ratio of de-Broglie wavelengths associated with them is

Moderate

A

$C (2 m E)^{\frac{1}{2}}$
B

$\frac{1}{c} {(\frac{2 m}{E})}^{\frac{1}{2}}$
C

$\frac{1}{c} {(\frac{E}{2 m})}^{\frac{1}{2}}$
D

${(\frac{E}{2 m})}^{\frac{1}{2}}$
(c being velocity of light)

Solution

For electron of energy E
$de-Broglie wavelength, λ_{e} = \frac{h}{p} = \frac{h}{\sqrt{2 m E}}$
For photon of energy, $E = h v = \frac{h c}{λ_{p}}$
$\Rightarrow λ_{p} = \frac{h c}{E}$
$∴ \frac{λ_{e}}{λ_{p}} = \frac{h}{\sqrt{2 m E}} \times \frac{E}{h c} = \frac{1}{c} {(\frac{E}{2 m})}^{1 / 2}$

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