SATHEE: Dual Nature of Radiation and Matter

Dual Nature of Radiation and Matter - Result Question 6

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

[2016]

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

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

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

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Answer:

Correct Answer: 6. (a)

Solution:

(a) For electron De-Broglie wavelength,

$λ_{e} = \frac{h}{\sqrt{2 m E}}$

For photon $E = p c$

$\Rightarrow$ De-Broglie wavelength, $λ_{P h} = \frac{h c}{E}$

$∴ \frac{λ_{e}}{λ_{P h}} = \frac{h}{\sqrt{2 m E}} \times \frac{E}{h c} = (\frac{E}{2 m})^{1 / 2} \frac{1}{c}$

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Dual Nature of Radiation and Matter - Result Question 6

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

Answer:

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