**Solutions: Radioactivity Questions**

**Q6**. A radioactive nuclide decays by emitting particles. The graph shows how the rate of decay A_{t} of the source changes with time t

(a) Determine

(i) the half-life of the nuclide,

From the graph - 50 seconds

(ii) the decay constant,

= ln 2 / 50 = 0.0139

= 0.014 s^{-1}(unit required!)

(iii) the initial number of undecayed nuclei present at time t = 0.

A_{t} = 0.24 MBq at time t = 0s

N = A/

= 0.24 x 10^{6}/0.0139

= 1.71 x 10^{7}

= 1.7 x 10^{7}

**(5 marks) **

(b) Each decay releases 1.0 x 10^{–12}J.

For the time interval between t = 30s and t = 80s, calculate:

(i) the number of nuclei which decay,

**At 30 seconds**

N = 1.71 x 10^{7} x e ^{(-0.014 x 30)}

N = 1.12 x 10^{7}

**At 80 seconds**

N = 1.71 x 10^{7} x e ^{(-0.014 x 80)}

N = 0.56 x 10^{7}

**during the time interval**

1.12 x 10^{7}- 0.56 x 10^{7} = 0.56 x 10^{7}

(ii) the energy released.

Total energy released = 0.56 x 10^{7} x 1.0 x 10^{–12}J

= 5.6 mJ

**(4 marks) **

**(Total 9 marks) **