An electron of mass and a photon have same energy . The ratio of de-Broglie wavelengths associated with them is (c being velocity of light) [2016]

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Q.
An electron of mass $m$ and a photon have same energy $E$ . The ratio of de-Broglie wavelengths associated with them is (c being velocity of light) [2016]

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

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

3 $\frac{1}{c} {(\frac{E}{2 m})}^{\frac{1}{2}}$

4 ${(\frac{E}{2 m})}^{\frac{1}{2}}$

Ans.
(3)

For electron of energy E,

de-Broglie wavelength, $λ_{e} = \frac{h}{p} = \frac{h}{\sqrt{2 m E}}$

For photon of energy, $E = h υ = \frac{h c}{λ_{p}} \Rightarrow λ_{p} = \frac{h c}{E}$

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

Solution

Q.
An electron of mass $m$ and a photon have same energy $E$ . The ratio of de-Broglie wavelengths associated with them is (c being velocity of light) [2016]

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

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

3 $\frac{1}{c} {(\frac{E}{2 m})}^{\frac{1}{2}}$

4 ${(\frac{E}{2 m})}^{\frac{1}{2}}$

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Solution

Q. An electron of mass m and a photon have same energy E. The ratio of de-Broglie wavelengths associated with them is (c being velocity of light) [2016]

1 c(2mE)12

2 1c(2mE)12

3 1c(E2m)12

4 (E2m)12

Ans. (3) For electron of energy E, de-Broglie wavelength, λe=hp=h2mE For photon of energy, E=hυ=hcλp⇒λp=hcE ∴ λeλp=h2mE×Ehc=1c(E2m)1/2

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Q.
An electron of mass $m$ and a photon have same energy $E$ . The ratio of de-Broglie wavelengths associated with them is (c being velocity of light) [2016]

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

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

3 $\frac{1}{c} {(\frac{E}{2 m})}^{\frac{1}{2}}$

4 ${(\frac{E}{2 m})}^{\frac{1}{2}}$