Strontium-90 is a radioactive isotope having a half-life of 28.0 years. Strontium-90 has a density of 2.54 g cm-3.

Question 11

(a) Define the decay constant of a radioactive isotope. [2]

(b) Strontium-90 is a radioactive isotope having a half-life of 28.0 years. Strontium-90 has a density of 2.54 g cm^-3.

A sample of Strontium-90 has an activity of 6.4 × 10⁹ Bq. Calculate

(i) the decay constant λ, in s^-1, of Strontium-90, [2]

(ii) the mass of Strontium-90 in the sample, [4]

(iii) the volume of the sample. [1]

(c) By reference to your answer in (b)(iii), suggest why dust that has been contaminated

with Strontium-90 presents a serious health hazard. [2]

Reference: Past Exam Paper – June 2007 Paper 4 Q6

Solution:

(a) The decay constant is the probability of decay of a nucleus per unit time.

(b)

(i)

{λ = ln 2 / t_1/2   where t_1/2 is the half-life of the isotope.

Since the decay constant is asked in s^-1, the half-life should also be in seconds.

28 years = 28 × 365 days = 28 × 365 × 24 hours = 28 × 365 × 24 × 3600 seconds}

λ = ln2 / (28×365×24×3600)         

λ = 7.85×10^-10 s^-1                                        

(ii)

A = (–) λN

{N is the number of nuclei in the sample.}

N = (6.4×10⁹) / (7.85×10^-10)

N = 8.15×10¹⁸                              

{The mass of 1 mole of Strontium-90 is 90 g.

But, 1 mole of any element contains 6.02×10²³ nuclei (atoms).

So, the mass of 6.02×10²³ nuclei is 90 g.

6.02×10²³ nuclei - - - > 90 g

1 nucleus - - - > 90 / (6.02×10²³)

8.15×10¹⁸ nuclei - - - > (8.15×10¹⁸×90) / (6.02×10²³)}

mass = (8.15×10¹⁸×90) / (6.02×10²³)

mass = 1.22×10^-3 g              

(iii)

{Density = mass / volume

Volume = mass / density}

volume = (1.22×10^-3 / 2.54 =) 4.8×10^-4 cm³              

(c)

EITHER The very small volume of Strontium-90 would have a high activity

OR The dust can be highly radioactive         

So, breathing in the dust presents health hazard