Question

Determine the kinetic energy of photons whose De Broglie wavelength is 90% smaller than photons of the same energy.

Answer 1

$$\lambda_e=0.9\lambda\\\frac{\sqrt{E^2-m_e^2c^4}}{hc}=0.9\frac{E}{hc}\\ E^2-m_e^2c^4=0.81E^2\\0.19E^2=m_e^2c^4\\0.19(K^2+m_e^2c^4)=m_e^2c^4\\ 0.19(K^2+0.511^2)=0.511^2\\K=1.055\ MeV$$