Ncert Exercises & Solutions

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

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

(i) Plot the graph of R versus t and calculate half-life from the graph.

(ii) Plot the graph of $\ln (\frac{R}{R_{0}})$ versus t and obtain the value of half-life from the graph.

Hint: The decay rate depends on the active nuclei.

Step 1: Find the value of

\ln (\frac{R}{R_{0}})

In the table given below, we have listed values of

R ({MB}_{q})

and

\ln (\frac{R}{R_{0}})

Step 2: Draw the graph between R and t.

(i) When we plot the graph of R versus t, we obtain an exponential curve as shown.

From the graph, we can say that activity R reduces to 50% in t = OB $\approx$ 40 min

So, $t_{1 / 2} \approx 40 \min .$

Step 3: Draw the graph between $\ln (\frac{R}{R_{0}})$ and t.

(ii) The adjacent figure shows the graph of $\ln (\frac{R}{R_{0}}) versus t .$

The slope of this graph $= - λ$

From the graph, $λ = - (\frac{- 4.16 - 3.11}{1}) = 1.05 h^{- 1}$

$Half - life, T_{1 / 2} = \frac{0.693}{λ} = \frac{0.693}{1.05} = 0.66 h = 39.6 \min \approx 40 \min$