Question

A photon and an electron have an equal energy ‘E’. The ratio of wavelength ‘λ_p’ of photon to that of electron ‘λ_e’ is proportional to ______.

Options

• `sqrt E`

• `1/sqrt E`

• `1/E`

• E

Answer 1

A photon and an electron have an equal energy ‘E’. The ratio of wavelength ‘λ_p’ of photon to that of electron ‘λ_e’ is proportional to `bbunderline(1/sqrt E)`.

Explanation:

De-Broglie wavelength, for an electron,

λ = `h/p`

= `h/sqrt (2 m_e E)`

For a photon,

E = `(hc)/lambda_p`

λ_p = `(hc)/E`

∴ `lambda_p/lambda_e = (hc)/E xx sqrt(2 m_e E)/h`

∴ `lambda_p/lambda_e prop 1/sqrt E`