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Question
Samples of two radioactive nuclides A and B are taken. λA and λB are the disintegration constants of A and B respectively. In which of the following cases, the two samples can simultaneously have the same decay rate at any time?
- Initial rate of decay of A is twice the initial rate of decay of B and λA = λB.
- Initial rate of decay of A is twice the initial rate of decay of B and λA > λB.
- Initial rate of decay of B is twice the initial rate of decay of A and λA > λB.
- Initial rate of decay of B is the same as the rate of decay of A at t = 2h and λB < λA.
Options
a and c
a and d
b and d
a and b
Solution
b and d
Explanation:
Law of radioactive disintegration: According to Rutherford and Soddy law for radioactive decay is as follows:
At any instant, the rate of decay of radioactive atoms is proportional to the number of atoms present at that instant.” i.e.
dN/dt ∞ N ⇒ dN/dt = – λN
it can be proved that N = N0e–λ1
In terms of mass M – M0e–λ1
where N = Number of atoms that remain undecayed after time t,
N0 = Number of atoms present initially (i.e., at t = 0),
M = Mass of radioactive nuclei at time t,
M0 = Mass ofradioactive nuclei at time t = 0,
N0 – N= Number of the disintegrated nuclei in time t,
dN/dt= rate of decay, λ = Decay constant or disintegration constant or radioactivity constant or Rutherford Soddy’s constant or the probability of decay per unit time of a nucleus.
The samples of the two radioactive nuclides A and B can simultaneously have the same decay rate at any time if the initial rate of decay of A is twice the initial rate of decay of B and λA > λB.
Also, when the initial rate of decay of B is the same as the rate of decay of A at t = 2h and λB < λA.
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