An isolated metal sphere of radius r is charged so that the electric potential at its surface is V₀. [Figure 5.1] On Fig. 5.1, sketch the variation with distance x from the centre of the sphere of the electric potential. Your graph should extend from x = 0 to x = 3r. Photons having wavelength λ are incident on a metal surface. The maximum wavelength for which there is emission of electrons is λ₀. For photons of wavelength λ₀/2, the maximum kinetic energy of the emitted electrons is E_MAX. On [Figure 5.2], sketch the variation with wavelength λ of the maximum kinetic energy for values of wavelength between λ = λ₀/3 and λ = λ₀. A pure sample of a radioactive isotope contains N₀ nuclei. The half-life of the isotope is T½. The product of the radioactive decay is stable. The variation with time t of the number N of nuclei of the radioactive isotope is shown in [Figure 5.3].

1. (c)On [Figure 5.3]: • label, on the time axis, the time t = 1.0T½ and the time t = 2.0T½ • sketch the variation with time t of the number of nuclei of the decay product for time t = 0 to time t = T.[3]

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