A photon and an electron (mass ) have the same energy . The ratio of their de-Broglie wavelengths is ( is the speed of light) [2025]

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Q.
A photon and an electron (mass $m$ ) have the same energy $E$ . The ratio $(λ_{photon} / λ_{electron})$ of their de-Broglie wavelengths is ( $c$ is the speed of light) [2025]

1 $c \sqrt{\frac{2 m}{E}}$

2 $\frac{1}{c} \sqrt{\frac{E}{2 m}}$

3 $\sqrt{\frac{E}{2 m}}$

4 $c \sqrt{2 m E}$

Ans.
(1)

$λ_{ph} = \frac{h c}{E}$ ...(i)

$λ_{e} = \frac{h}{p} = \frac{h}{\sqrt{2 m E}}$ ...(ii)

From eqn. (i) and (ii), we get

$∴$ $\frac{λ_{ph}}{λ_{e}} = \frac{h c \sqrt{2 m E}}{E . h} = c \sqrt{\frac{2 m}{E}}$

Solution

Q.
A photon and an electron (mass $m$ ) have the same energy $E$ . The ratio $(λ_{photon} / λ_{electron})$ of their de-Broglie wavelengths is ( $c$ is the speed of light) [2025]

1 $c \sqrt{\frac{2 m}{E}}$

2 $\frac{1}{c} \sqrt{\frac{E}{2 m}}$

3 $\sqrt{\frac{E}{2 m}}$

4 $c \sqrt{2 m E}$

Ans.
(1)

$λ_{ph} = \frac{h c}{E}$ ...(i)

$λ_{e} = \frac{h}{p} = \frac{h}{\sqrt{2 m E}}$ ...(ii)

From eqn. (i) and (ii), we get

$∴$ $\frac{λ_{ph}}{λ_{e}} = \frac{h c \sqrt{2 m E}}{E . h} = c \sqrt{\frac{2 m}{E}}$

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Solution

Q. A photon and an electron (mass m) have the same energy E. The ratio (λphoton/λelectron) of their de-Broglie wavelengths is (c is the speed of light) [2025]

1 c2mE

2 1cE2m

3 E2m

4 c2mE

Ans. (1) λph=hcE ...(i) λe=hp=h2mE ...(ii) From eqn. (i) and (ii), we get ∴ λphλe=hc2mEE.h=c2mE

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Q.
A photon and an electron (mass $m$ ) have the same energy $E$ . The ratio $(λ_{photon} / λ_{electron})$ of their de-Broglie wavelengths is ( $c$ is the speed of light) [2025]

1 $c \sqrt{\frac{2 m}{E}}$

2 $\frac{1}{c} \sqrt{\frac{E}{2 m}}$

3 $\sqrt{\frac{E}{2 m}}$

4 $c \sqrt{2 m E}$

Ans.
(1)

$λ_{ph} = \frac{h c}{E}$ ...(i)

$λ_{e} = \frac{h}{p} = \frac{h}{\sqrt{2 m E}}$ ...(ii)

From eqn. (i) and (ii), we get

$∴$ $\frac{λ_{ph}}{λ_{e}} = \frac{h c \sqrt{2 m E}}{E . h} = c \sqrt{\frac{2 m}{E}}$