Question

The activity R of an unknown radioactive nuclide is measured at hourly intervals. The results found are tabulated as follows:

t (h)	0	1	2	3	4
R (MBq)	100	35.36	12.51	4.42	1.56

1. Plot the graph of R versus t and calculate the half-life from the graph.
2. Plot the graph of ln `(R/R_0)` versus t and obtain the value of half-life from the graph.

Answer 1

We have listed R(MB_q) and In `(R/R_0)` in the table below.

t (h)	0	1	2	3	4
R (MBq)	100	35.36	12.51	4.42	1.56
`R/R_0`	–	– 1.04	– 2.08	– 3.11	– 4.16

i. Graph between R versus t is an exponential curve. From the graph at slightly more than `t = 1/2 h` the R should be 50% so at R = 50% the t(h) = 0.7h

= 0.7 × 60 min

= 42 min

ii. The adjacent figure shows the graph of In `(R/R_0)` versus t.

The slope of this graph = – λ

From the graph,

`λ = - ((-4.16 - 3.11)/1) = 1.05  h^-1`

Hence half-life `T_(1/2) = 0.693/λ  = 0.693/1.05` = 0.66 h

= 39.6 min ≈ 40 min