A GM tube placed close to a radium source gives an initial average corrected count rate of 334 s^-1

(a)     The GM tube detects 10 % of the radiation.  What is the initial activity?

(b)    Initially there were 1.5 ´ 10⁹ nuclei in the sample.  What is the decay constant?

(c)     What is the half life of the radium in days?                                                

(a) The activity is 334 ¸ 0.1 = 3340 s^-1 (P)

(b) DN/Dt = -lN (P)

-3340 = -l ´ 1.5 ´ 10⁹ = 2.23 ´ 10^-6 s^-1 (P)

(c) N = No e^-lt

½ = e^{-2.23 ´ 10^-6 ´t}

loge ½ = -2.23 ´ 10^-6 ´ t (P)

t = -0.693 ¸ 2.23 ´ 10^-6 = 3.1 ´ 10⁵ s

t = 3.6 days (P)