Calculate the energy of one X-ray photon.

Here are the solutions to your questions: 1) a) Calculate the maximum velocity of electrons that would produce X-rays of frequency 8 × 10^18 Hz if only 80% of kinetic energy is converted to X-rays. (Take h = 6.63 × 10^-34 Js and mass of electron m_e = 9.1 × 10^-31 kg) Step 1: Calculate the energy of one X-ray photon. E_photon = hf E_photon = (6.63 × 10^-34 Js) × (8 × 10^18 Hz) E_photon = 5.304 × 10^-15 J Step 2: Determine the total kinetic energy of the electron required, considering the 80% conversion efficiency. E_photon = 0.80 × KE_electron KE_electron = E_photon0.80 KE_electron = 5.304 × 10^-15 J0.80 KE_electron = 6.63 × 10^-15 J Step 3: Use the kinetic energy to find the maximum velocity of the electron. KE_electron = (1)/(2) m_e v^2 v = sqrt(2 × KE_electron)m_e v = sqrt(2 × (6.63 × 10^-15) J)9.1 × 10^-31 kg v = sqrt(1.45714 × 10^16) v ≈ 1.21 × 10^8 m/s The maximum velocity of the electrons is 1.21 × 10^8 m/s. b) An X-ray tube operating at a P.D. of 50 kV has a tube current 20 mA. Calculate: (i) The electric input (ii) The number of electrons hitting the target per second given that e = 1.6 × 10^-19 C (iii) The velocity of electrons when they hit the target. Given: Potential difference, V = 50 kV = 50 × 10^3 V Current, I = 20 mA = 20 × 10^-3 A Charge of an electron, e = 1.6 × 10^-19 C Mass of electron, m_e = 9.1 × 10^-31 kg (i) The electric input Step 1: Calculate the electric