Question 13
The isotope iodine-131
(13153I) is radioactive with a decay constant of 8.6 ×
10-2 day-1.
β- particles are emitted with a maximum energy of
0.61 MeV.
(a)
State what is meant by
(i)
radioactive, [2]
(ii)
decay constant. [2]
(b)
Explain why the emitted β- particles have a range of energies. [2]
(c)
A sample of blood contains 1.2 × 10-9 g of iodine-131.
Determine, for this
sample of blood,
(i)
the activity of the iodine-131, [3]
(ii)
the time for the activity of the iodine-131 to be reduced to 1/50 of
the activity calculated in (i). [2]
[Total: 11]
Reference: Past Exam Paper – November 2017 Paper 42 Q12
Solution:
(a)
(i)
A radioactive nucleus is an unstable nucleus that emits
particles / EM radiation / ionizing radiation randomly and spontaneously.
(ii)
The decay constant is the probability of decay of a
nucleus per unit time.
(b)
The emitted beta particle has to share the energy of the
disintegration with the emitted antineutrino.
(c)
(i)
{A = λN
We need to find the value of N.
The relative atomic mass of iodine is 131 g.
This mass contains 6.02 × 1023 nuclei.
131 g - - - > 6.02 × 1023 nuclei
1.2×10-9
g - - - > [(1.2 × 10-9)
/ 131] × 6.02 × 1023 nuclei}
number = [(1.2 × 10-9) / 131] × 6.02
× 1023
number ( = 5.51 × 1012)
A = λN
{Decay constant λ = 8.6×10-2
day-1
We need to convert the decay constant from day-1
to s-1.
In a day, there are (24 × 3600) seconds.
Decay constant λ = 0.086 / (24 × 3600)
s-1 }
A = [0.086 / (24 × 3600)] × 5.51
× 1012
A = 5.5 × 106 Bq
(ii)
{A = A0 exp(-λt)
A / A0 = exp(-λt) and A / A0 = 1 / 50}
1 / 50 = exp(–0.086t)
{1 / 50 = exp(–0.086t)
ln (1/50) = –0.086t }
t = 45 days
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