XII Physics Midnight Numericals 1. Calculate the root mean square speed of molecules at 0°C and 1.0 atm pressure. Assuming hydrogen to be an ideal gas. The density of hydrogen is 8.99 × 10⁻² kg/m³. 2. A heat engine works at the rate of 500 kW. The efficiency of the engine is 30%. Calculate the loss of heat per hour. 3. X-rays with an energy of 300 keV undergo Compton scattering with a target. If the scattered X-rays are detected at 30° relative to the incident X-rays: Determine the Compton shift at this angle. Find the energy of the scattered X-rays. Calculate the energy of the recoiling electron. 4. A solenoid has length L = 1.23 m and inner diameter d = 3.55 cm, and it carries a current I = 5.57 A. It consists of five close-packed layers, each with 850 turns along length L. What is the magnetic field (B) at its center? 5. A capacitor of 200 pF is charged to a potential difference of 100 V. Its plates are then connected in parallel to another capacitor, and the potential difference becomes 60 V. Find the capacitance of the second capacitor. 6. A 50 g piece of copper at 100°C is placed in 200 g of water at 20°C. If the final temperature of the system is 21.8°C, calculate the specific heat capacity of copper. (Specific heat of water = 4.18 J/g°C) 7. In an RLC circuit, R = 50 Ω, L = 0.1 H, and C = 50 μF. Calculate the resonance frequency. 8. The half-life of ₁₀₄P²⁰¹₀ is 140 days. By what percentage does its activity decrease per week? OR Alpha particles are accelerated from rest at a potential difference of 1 kV, then they enter a magnetic field B = 0.2 T at an angle of 45° to the magnetic field. Calculate the radius of the path. 9. In an RL circuit, R = 30 Ω and L = 0.2 H. Calculate the total impedance at a frequency of 60 Hz. 10. What is the coefficient of performance (COP) of a refrigerator that operates between temperatures -3.00°C and +27.0°C? OR A heat engine works at the rate of 500 kW. The efficiency of the engine is 30%. Calculate the loss of heat per hour.