A radio active element has rate of disintegration 8000 disintegrations per minute at a particular instant. After four minutes it becomes 2000 disintegrations per minute. The decay constant per minute is

Step-by-step solution

The rate of radioactive disintegration follows exponential decay: R = R₀ e^ - t . Given R₀ = 8000 and R = 2000 after t = 4 minutes, we solve for : 2000 = 8000 e^ -4 Simplifying gives 1 4 = e^ -4 . Taking natural logarithms: ( 1 4 ) = -4 Expanding: - 4 = -4 Thus = 4 4 = (2^2) 4 = 1 2 2 This matches option C .