7. (a) A radioactive sample contains 530 x 10 g of nobelium-259, which has a half-life of 59 min. i) How many atoms of nobelium-259 are in the sample initially? ii) What is the initial activity of the sample? iii) What is the activity of the sample after 8h? [10] (b) What is meant by total internal reflection of light? State the conditions under which it occurs. Define critical angle and explain how the critical angle for a material in air depends on its refractive index. [5] (c) A ray of light is incident on the face AC of a glass prism, n = 1.51 as shown in Figure 7.1. (Air) n = 1.00 Figure 7.1 A n = 1.51 B i) What is the angle of refraction at the surface AC? ii) What is the angle of incidence on the surface BC?5. (a) Show clearly by means of ray diagrams how a concave mirror produces i) an upright image. an inverted image. 16] (b) Find the size and the position of the image of an object Sem high placed 12dem from a convex mirror with a focal length of magnitude 40cm. 141 (c) Figure 5.1 shows a plastic lens of refractive index 1.50, having a convex surface of radius 20cm and a concave surface of radius 40cm. Compute the focal length of the lens and state whether it is converging or diverging. 141 20cm 40cm Figure 5.1 (d) An object 2cm high is placed upright on the principal axis 20em to the left of the lens shown in Figure 5.1. D) Find the position of the image formed by the lens. State the nature of the image. Find the height of the image. 1616. (d) Consider the fission of uranium-235 in accordance with the nuclear equation: 235 141 X U 92 Ba + y 36 Kr + 3 n What are the values of the quantities labelled x and y in the reaction? ii) Calculate the energy released in a single fission reaction. 171 Symbol Atomic Mass (u) 235 U 235. 04393 92 Kr 91.92620 36 141 Ba 140.91440 1 1.00867 (e) Given that r. = 1.2 x 10 15m, estimate the radius of the %% 235 U nucleus. 13]