A radioactive element has rate of disintegration 16 , 000 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 disintegration (activity) of a radioactive element follows the exponential decay law: A = A₀ e^ - t Given initial activity A₀ = 16000 disintegrations per minute, final activity A = 2000 disintegrations per minute, and time t = 4 minutes. Substituting these values into the equation: 2000 = 16000 e^ - (4) 2000 16000 = e^ -4 1 8 = e^ -4 Taking the natural logarithm on both sides: _e ( 1 8 ) = -4 _e(2⁻³) = -4 -3 _e 2 = -4 = 3 4 _e 2 = 0.75 _e 2