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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