An electron of mass m and a photon have same energy E. The ratio of de-Broglie wavelengths associated with them is

Options

(a) (E/2m)¹∕₂
(b) c(2mE)¹∕₂
(c) 1/c (2m/E)¹∕₂
(d) 1/c (E/2m)¹∕₂

Correct Answer:

1/c (E/2m)¹∕₂

Explanation:

λₑ = h / √2mE,

λ_p = hc / E,

E = hc / λ_p

λₑ / λ_p = (h / √2mE) (E / hc)

= 1/c √(E / 2m)

=1/c (E/2m)¹∕₂