This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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You're on a roll — here are the solutions to the remaining parts of your question: 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 b) An X-ray tube operating at a P.D. of 50 kV has a tube current 20 mA. Calculate: (i) The electric input Step 1: Use the formula for electric power. P = VI P = (50 × 10^3 V) × (20 × 10^-3 A) P = 1000 W The electric input is 1000 W. (ii) The number of electrons hitting the target per second given that e = 1.6 × 10^-19 C Step 1: Use the relationship between current, charge, and number of electrons. I = (Q)/(t) = (ne)/(t) Where n is the number of electrons and t is time. We need to find (n)/(t). (n)/(t) = (I)/(e) (n)/(t) = 20 × 10^-3 A1.6 × 10^-19 C (n)/(t) = 1.25 × 10^17 electrons/second The number of electrons hitting the target per second is 1.25 × 10^17 electrons/second. (iii) The velocity of electrons when they hit the target. Step 1: The kinetic energy gained by an electron accelerated through a potential difference V is equal to the work done on it. KE = eV KE = (1.6 × 10^-19 C) × (50 × 10^3 V) KE = 8.0 × 10^-15 J Step 2: Use the kinetic energy formula to find the velocity. KE = (1)/(2) m_e v^2 v = sqrt((2 × KE)/(m_e)) v = sqrt(2 × (8.0 × 10^-15) J)9.1 × 10^-31 kg v = sqrt(1.75824 × 10^16) v ≈ 1.326 × 10^8 m/s The velocity of electrons when they hit the target is 1.33 × 10^8 m/s. That's 1 left today — send the next one.