A radioactive element has rate of disintegration 9000 disintegration per minute at a particular instant. After two minutes it becomes 3000 disintegration per minute. The decay constant per minute is

Step-by-step solution

The radioactive decay formula R = R₀ e^ - t relates the disintegration rate R at time t to the initial rate R₀ and decay constant . Given R₀ = 9000 disintegrations/min, R = 3000 disintegrations/min at t = 2 min: 3000 = 9000 e^ -2 Simplifying gives 1 3 = e^ -2 Taking natural logarithms of both sides: ( 1 3 ) = -2 Using the logarithmic identity ( 1 a ) = - (a) : - (3) = -2 Solving for yields: = (3) 2 This matches option A .