The de-Broglie wavelength of a particle having kinetic energy E is λ . How much extra energy must be given to this particle so that the de-Broglie wavelength reduces to 75 % of the initial value?

Step-by-step solution

Recall the formula of de-Broglie wavelength, λ = h p , here p is the linear momentum of the particle, now use the relation between linear momentum and kinetic energy, p = 2 E m ⇒ E ∝ 1 λ 2 ⇒ E = k λ 2 and   E ' = 16 k 9 λ 2 ⇒ Δ E = 7 E 9 .