# The disintegration rate of a radioactive sample at a certain instant is 4750 dpm . Five minute later rate becomes 2700 disintegration per minute ; Then the half-life of sample is

$(a)\;12.26 min\qquad(b)\;6.13 min\qquad(c)\;3.06 min\qquad(d)\;7.92 min$

Answer : $\;6.13\; min$
Half life is given by $T_{\frac{1}{2}}=\large\frac{\log_{e}^{2}}{\lambda}$
$=\large\frac{0.693}{0.1131}$$=6.13\; min\;.$
edited Aug 12, 2014