Physics

Problem

To determine the half-life of a radioactive element, a student plots a graph of

\ln \left| \frac{dN(t)}{dt} \right|

versus

t

. Here

\frac{dN(t)}{dt}

is the rate of radioactive decay at time

t

. If the number of radioactive nuclei of this element decreases by a factor of

p

after 4.16 years, the value of

p

is: (Take

e^{2.08} = 8

)