The energy of a photon is equal to the kinetic energy of a proton. If ₁ is the de-Broglie wavelength of a proton, ₂ the wavelength associated with the proton and if the energy of the photon is E , then ( ₁ / ₂ ) is proportional to

Step-by-step solution

We know that, de-Broglie wavelength of photon E=h v But we know that also aligned E & = 1 2 m v^2 2 E & = P^2 m P & =m v P^2 m & =m v^2 P & = 2 m E aligned (for proton) According to the question ₁= h P (de-Broglie of matter waves) and ₂= h c E From the Eqs. (ii) and (iii), we get aligned ₁ ₂ & = h / P h c / E = E P_C & = E 2 m E C = E 2 m C aligned array ll So, & ₁ ₂ = E 2 m c & ₁ ₂ E & ₁: ₂=E^ 1 / 2 array