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YOUR PARTICIPATION FOR THE GROWTH OF PHYSICS REFERENCE BLOG

Tuesday, February 5, 2019

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 / t1/2   where t1/2 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

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