O lvl Phy: Radioactivity

Radium-228 is a radioactive isotope which decays by α-emission to an isotope of radon (Rn). Two further α-emissions give in turn isotopes of polonium (Po) and lead (Pb). The lead isotope normally decays by β-emission to an isotope of bismuth (Bi). There is significant γ-emission with the decays of the radium and the lead.

The atomic number of radium (Ra) is 88.

(a) Write the nuclear equation of the decay of radium (Ra) to radon (Rn).

(b) Fill up the table below showing the nucleon (mass) numbers, proton (atomic) numbers and neutron numbers of the elements described above.

(c) The decay of 16 g of lead (Pb) to 14 g bismuth (Bi) takes 66.9 years. Find the half life of the radioactive of lead (Pb).

*************************

Answer:

(a)



(b)



(c) Since mass num of Pb is same as mass num of Bi, 16 g of Pb will decay to 16 g of Bi eventually.
Since there is 14 g of Bi, it means 2 g of Pb is left.

16 g Pb -> 8g Pb -> 4g Pb -> 2g Pb
Hence, 3 half lives = 66.9 years
Half-life = 22.3 years

O lvl Phy: Radioactivity

N atoms of isotopes phosphorus-32 undergo radioactive decay. It decays to a non radioactive sulphur-32. Calculate in terms of N, the number of phosphorus-32 atoms remaining at the end of the 60 days, given that the half life of the isotope is 15 days.

*************************

Answer:

15 days --> 1 half-life
30 days --> 2 half-life
45 days --> 3 half-life
60 days --> 4 half-life

so,
N --> N/2 --> N/4 --> N/8 --> N/16

Thus, N/16 of phosphorus-32 atoms is left at the end of the 60 days

O lvl Phy: Radioactivity

It is known that one gram of carbon from a living plant which contains a definite proportion of carbon-14 decays at a rate of 15 disintegration per minute. a specimen which was formed from a living plant a long time ago shows 15 disintegration every 4 minutes from one gram of carbon present in it.

Given that the count rate from carbon-14 begins to fall only when tree dies, estimate the age of the specimen. (the half life of carbon-14 is 5000 years)

*************************

Answer:

Specimen is now at15 disintegrations/4 min


Starting from 15 disintegrations / min when it was still living

After one half life:
it would have been 15 disintegrations per 2 minutes

After a 2nd half life:
15 disintegrations per 4 minutes

Thus, the specimen had went through 2 half lives.
So 5000*2 = 10000 years