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  • A photon and an electron have got the same de broglie wavelength. Which of the following is correct<img alt="\mathrm{ \left(E_1=\right. energy \ of \ photon ), E_2=energy \ of \ electron.}" src="ht

A photon and an electron have got the same de broglie wavelength. Which of the following is correct\mathrm{ \left(E_1=\right. energy \ of \ photon ), E_2=energy \ of \ electron.}

Option: 1

\mathrm{E_1>E_2}


Option: 2

\mathrm{E_1=E_2}


Option: 3

\mathrm{E_1<E_2}


Option: 4

None of the above


Answers (1)

best_answer

Let \lambda  is their debroglie wavelength 

\mathrm{\Rightarrow \text { For electron } \lambda=\frac{h}{m v}}

 Energy of photon having wavelength 

\mathrm{\lambda \text { is } E_1=\frac{h c}{\lambda}=h c \times \frac{m v}{h}=m v c \text {. (1) }}

According to Einstein's mass -energy equivalence, the energy of electron

\mathrm{\text { is } E_2=m c^2=m c \times c \text {. }}

\mathrm{\begin{aligned} \text { since } & c>v \\ \Rightarrow E_2 & >E_1 . \end{aligned}}

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