Question

The count rate of nuclear radiation coming from a radiation coming from a radioactive sample containing 128I varies with time as follows. Time t (minute)
0
25
50
75
100
Ctount rate R (109 s−1)
30
16
8.0
3.8
2.0
(a) Plot In (R0/R) against t. (b) From the slope of the best straight line through the points, find the decay constant λ. (c) Calculate the half-life t1/2.

Answer 1

Explanation:

(a) When t = 0,

When the time is 25 s $\rightarrow \ln \mathrm{ROR}=0$,

When the time is 50 s$\rightarrow \ln \mathrm{ROR} 2=0.63$,

When the time is 75 s $\rightarrow \ln \mathrm{ROR} 3=1.35$

When the time is 100 s $\rightarrow \ln \mathrm{ROR} 4=2.06$

$\ln \mathrm{ROR} 5=\ln 30 \times 109 \times 1092=2.7$

The graph required is given here.

(b) Graph has the slope = 0.028

Therefore, the constant of decay, $\lambda=0.028 \mathrm{min}-1$

Half-life period T12 is shown as

$\mathrm{T} 12=0.693 \lambda=25 \mathrm{min}$