**Solutions: Radioactivity Questions**

**Q8. **The radioactive isotope of sodium has a half life of 2.6 years.

A particular sample of this isotope has an initial activity of 5.5 × 10^{5} Bq (disintegrations per second).

(a) Explain what is meant by the random nature of radioactive decay.

.

There is equal probability of any **nucleus **decaying, it cannot be known which particular nucleus will decay next.

The rate of decay is unaffected by the surrounding conditions,

It cannot be known at what time a particular **nucleus** will decay, it is only possible to estimate the proportion of **nuclei **decaying in the next time interval.

**(2 marks MAX) **

(b) On the axes below, sketch a graph of the activity of the sample of sodium over a period of 6 years.

Marks awarded for a continuous curve starting at 5.5 × 10^{5} Bq plus correct 1st half-life (2.6 yrs, 2.75 × 10^{5} Bq correct 2nd half-life (5.2 years, 1.4 × 10^{5} Bq)

**(2 marks) **

(c) Calculate

(i) the decay constant, in s^{–1}, of ,

*1 year = 3.15 × 10*^{7} s

= ln 2/(2.6 x 3.15 × 10^{7}) = 8.5 × 10^{–9} s^{–1 }

(ii) the number of atoms of in the sample initially,

Initial decay rate = N_{0}/t = 5.5 × 10^{5} Bq

N =5.5 × 10^{5}/ 8.5 × 10^{–9}

= 6.5 × 10^{13} (atoms)

(iii) the time taken, in s, for the activity of the sample to fall from 1.0 × 10^{5} Bq to 0.75 × 10^{5} Bq.

ln(0.75 × 10^{5} /1.0 × 10^{5} ) = - 8.5 × 10^{–9} x t

t = - (ln 0.75)/8.5 × 10^{–9}

= 3.4 × 10^{7} s

**(6 marks) **

**(Total 10 marks) **