The isotope iodine-131 (13153I) is radioactive with a decay constant of 8.6 × 10-2 day-1.

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