Question

According to de-Broglie hypothesis, the wavelength associated with moving electron of mass 'm' is 'λ_e'· Using mass energy relation and Planck's quantum theory, the wavelength associated with photon is  'λ_p'. If the energy (E) of electron and photon is same then relation between 'λ_e' and 'λ_p' is ______.

Options

• λ_p ∝ λ_e 

• λ_p ∝ λ_e²

• λ_p ∝ `sqrt (λ_e)`

• λ_p ∝ ` 1/λ_e`

Answer 1

According to de-Broglie hypothesis, the wavelength associated with moving electron of mass 'm' is 'λ_e'· Using mass energy relation and Planck's quantum theory, the wavelength associated with photon is  'λ_p'. If the energy (E) of electron and photon is same then relation between 'λ_e' and 'λ_p' is λ_p∝ λ_e. 

Explanation:

The wavelength associated with photon,

λ_p =`("hc")/"E"` ....(i)

The wavelength associated with the electron,

λ_p =`"h"/"p"`

But p =` "E"/"c"`

∴ λ_e =`("hc")/"E"` ....(ii)

From equation (i) and (ii),

λ_p ∝ λ_e