Discussion Forum



1)

According to the de-Broglie hypothesis, the wavelength associated with moving electron of mass 'm' is $\lambda_{e}$ '. Using mass-energy relation and planck's quantum theory, the wavelength associated with a photon is '$\lambda_{p}$ '. If the energy (E)  of electron and the photon is same, then the relation between '$\lambda_{e}$' and '$\lambda_{p}$' is 


A) $\lambda_{p}\propto \lambda_{e}$

B) $\lambda_{p}\propto \lambda_{e}^2$

C) $\lambda_{p}\propto \sqrt{\lambda_{e}}$

D) $\lambda_{p}\propto \frac{1}{\lambda_{e}}$

Answer:

Option A

Explanation:

The energy of photon  is given as,

  $E_{p}=\frac{hc}{\lambda_{p}}$

$\therefore$     $\lambda_{p}=\frac{hc}{E_{p}}$   ........(i)

 Energy of an moving electron is given as,

 $E_{e}=mc^2=pc\Rightarrow p=\frac{E_{p}}{c}$

$\therefore$    $\lambda_{e}=\frac{h}{p}=\frac{hc}{E_{e}}$   ........(ii)

 Given, Ep= Ee

 Therefore from Eqs.(i) and (ii) , we get   $\lambda_{p}\propto \lambda_{e}$