The following MCQ (on radioactivity) which appeared in Kerala Engineering Entrance 2007 question paper is simple, but it differs slightly from the conventional type:
Radium has half life of 5 years. The probability of decay of a radium nucleus in 10 years is
(a) 50% (b) 75% (c) 100% (d) 60% (e) 25%
Since the half life is 5 years, the amount getting decayed in 10 years will be 75%.
[This can be found very easily: After 5 years half the initial amount will be decayed; after another 5 years, half of the remaining will be decayed. If the half life and the time period given are not so simply related, you will have to calculate the number of nuclei undecayed (N) using the equation, N = N0/2n where N0 is the initial number and ‘n’ is the number of half lives in the given time. The percentage decayed in the given time is then calculated].
The probability for decay of any given nucleus in 10 years is therefore 75%.
The following question involving the relative abundance of isotopes is a popular one and it has found place in Kerala Engineering Entrance 2007 question paper:
The natural boron of atomic weight 10.81 is found to have two isotopes B10 and B11. The ratio of abundance of isotopes in natural boron should be
(a)
This is a simple arithmetical problem. If there are n1 boron atoms of atomic weight 10 and n2 boron atom of atomic weight 11 in a sample of natural boron, the mean atomic weight (which is given as 10.81) is related to n1 and n2 as
(10n1 + 11n2)/ (n1 + n2) = 10.81.
Rearranging, 0.81n1 = 0.19n2, from which n1/n2 = 19/81.
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