8   12 In February 2021 the spacecraft Perseverance Rover landed on Mars. When the spacecraft was 11.0 km above the surface of Mars, parachutes opened to slow the descent. The parachutes detached from the spacecraft when it was 2.1 km above the surface of Mars. Calculate the change in gravitational potential energy of the spacecraft during the parachute section of its descent. mass of spacecraft = 1030 kg mass of Mars = 6.39 × 1023 kg radius of Mars = 3390 km .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. Change in gravitational potential energy of the spacecraft = ...................................................... (Total for Question 12 = 3 marks) Turn over 9   13 Actinium-225 and bismuth-210 are radioactive isotopes. A sample of each isotope is prepared so that each sample has the same number of nuclei initially. Explain why the activity of each sample would be the same after 10 days. half-life of actinium-225 = 10 days half-life of bismuth-210 = 5 days .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (Total for Question 13 = 4 marks)