F6D Physics Test 4 (Radioactivity and Nuclear Physics) (15-16) Suggested Answers
1.(a)Decay constant is the probability of decay per unit time. OR
Decay constant is the fraction of atoms decaying per second.
(b)(1M+1M+1A)
(c)Number of nuclei = 3 x 1023 x 1/1012 = 3 x 1011(1M)
Rate of decay = A = kN = 3.84 x 10-12 x 3 x 1011
= 1.15 Bq(1A)
(d)A = A0 e -k t(1M)
(1M)
t = 4720 years(1A)
(e)The boat may have been made with the wood some time after the tree was cut down.
(That is, if the tree was cut down 4700 years ago, but the boat was made after 1000 years, then the age of the wood was found to be 4700 years, not agreed with the age of boat --- only 3700 years old)
The background activity is high compared with the observed count rates.
The count rates are low or sample mass is small so that there is statistical variation in the recorded result.
Uncertainty in the ratio of carbon-14 in carbon thousands of years ago.
Any two(2A)
2.(a)The half-life of a radioactive nuclide is the time taken for half of the nuclei in a sample to decay, or
the time taken for the activity of a sample to fall to half of its original value.
(b)(i)Radon 216 has too short a half life or decays too quickly.
It is difficult to measure the activity accurately.
(ii)Initial activity 560 (1A)
Curve showing exponential decay(1A)
280 at 2.4 min or
140 at 4.8 min(1A)
(iii)A = A0 e -k t
20 = 560 e-(ln 2 / 2.4) t(1M for k, 1M for formula)
t = 11.5 min(1A)
(c)Since ln A = ln Ao -kt
A plot of ln A against t is a straight line with slope = -k(1M)
Half life = ln 2 / k = -0.693 / slope of graph(1A)
MC1-5 D D D C A6-10 D D B D D11-15 C B B D C16 A
Explanations to selected MC
3.Radon gas in air contributes background radiation, although the amount is not too great.
4. Alpha particles are helium nuclei, not helium atoms.
8.(1) is radioactive decay, not fission.
11.After inserting a piece of paper, the reading drops significantly, so there must be alpha radiation. Similarly, after inserting a 25 mm lead, the reading drops significantly, so there must be gamma radiation.
14.The unit of Sv has already taken all factors into consideration. Same dose means same harm (same probability of getter cancer).
15.Energy released = m c2
= (2.01472 + 3.01697 – 4.00391 – 1.00897) x 931 = 17.5 MeV = 2.81 x 10-12 J