Physics Test 2 (Radioactivity) Suggested Answers
1. (a) For U, a graph starting at 3 x 1022 showing exponential fall passing through 1.5 x 1022 near 4.5 x 109 years.
For Pb, an inverted graph of the above so that the graphs cross at 1.5 x 1022 near 4.5 x 109 years.
(b) Let u represent the number of uranium atoms, then
u
2
3  10 22  u
u = 2 x 1022 atoms
(c) N = N0ekt
2 x 1022 = 3 x 1022 x e-kt
t = ln 1.5 / k
k = ln 2 / 4.5 x 109 = 1.54 x 10-10 (1M)
t = 2.6 x 109 years
(1A)
2. (a) Decay constant is the probability of decay per unit time. OR
Decay constant is the fraction of atoms decaying per second.
(b) t 1 =
2
ln 2
ln 2

 1.81  1011 s  5730 years
k
3.84  10 12
(c) Number of nuclei = 3 x 1023 / 1 x 1012 = 3 x 1011
Rate of decay A = kN = 3.84 x 10-12 x 3 x 1011
= 1.15 Bq
kt
(d) A = A0e
12
0.65  1.15e 3.8410
t
T = 4720 years
(e) The boat may have been made with the wood some time after the tree was cut down.
The background activity is high compared to the observed count rates
The count rates are low or sample size / mass is small or there is statistical variation in the recorded results.
Possible contamination, for example, other radioactive substances mixed with the wood.
Uncertainty in the ratio of carbon-14 in carbon thousands of years ago.
MC
1-5 B C B C B
6-10 D B B C B
11-12 C A
Explanations to selected MC
1. Gamma rays do not carry charges and so are not deflected by magnetic field.
3. Right angled fork track is seen in the chamber. The tracks are straight and thick, indicating that these must be
due to alpha particles and the gas inside must be helium, nearly same mass as alpha particles.
Statement 2 is incorrect because alcohol vapour condenses on ion pairs produced by alpha particles, but not
directly on alpha particles.
4. Y emits gamma ray because after the insertion of lead, the reading reduces to 100, but is still higher than the
background count rate (60 c.p.m.), showing that some gamma ray still contributes to the count rate apart from
background count rate.
Z emits beta radiation because the reading drops to background count rate.
6. Putting a piece of paper does not cause a drop in reading because the GM tube is 10 cm away from the source,
already longer than the range of alpha particles.
7. T must be due to beta particles because beta particles are lighter and deflect more than alpha particles.
Q must be due to alpha particles because alpha particles suffer a less deflection.
If the direction of magnetic field is opposite, then alpha particles would go to S while beta particles would go to
P.
8. Background count rate is 100 cpm.
500  400
300  200
From 500 to 300, the time is 2 min.
9. N = N0ekt  40e

ln 2
2
4
 28.3
12. kX > kY, => tX < tY, so Statement 1 is correct.
A = kN, the activity depends on two factors, not just k. So Statement 2 is incorrect.