FOLLOW US ON TWITTER
SHARE THIS PAGE ON FACEBOOK, TWITTER, WHATSAPP ... USING THE BUTTONS ON THE LEFT


YOUR PARTICIPATION FOR THE GROWTH OF PHYSICS REFERENCE BLOG

Thursday, February 28, 2019

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

No comments:

Post a Comment

If it's a past exam question, do not include links to the paper. Only the reference.
Comments will only be published after moderation

Currently Viewing: Physics Reference | The isotope iodine-131 (13153I) is radioactive with a decay constant of 8.6 × 10-2 day-1.