A point source emitting alpha particles is situated at a distance of 1 m from a counter that registers any alpha particle striking its 1 cm ^2 window. Given that the source has 6.0 10¹⁶ active nuclei and the counter registers a rate of 50000 counts/second , determine the decay constant. Assume the source radiates alpha particles uniformly in all directions and that the alpha particles strike the window nearly normall

Step-by-step solution

The total activity of the source is given by A₀ = N , where is the decay constant and N is the number of active nuclei. Since the alpha particles are emitted uniformly in all directions, the fraction of particles hitting the window is the ratio of the area of the window to the total surface area of a sphere of radius r . Fraction of particles registered = A 4 r^2 The count rate C is the number of alpha particles striking the window per second: C = A₀ A 4 r^2 = N A 4 r^2 Rearranging for the decay constant : = C 4 r^