Half life of a radioactive substance ′A′ is 4 days.The probability that a nucleus will decay in two half
Half life of a radioactive substance ′A′ is 4 days.The probability that a nucleus will decay in two half
The correct option is B 34
After every half-life of time, there is a 50% probability that any given nucleus will decay.
So after one-half-life, there is a 50% probability that a particular nucleus will have decayed. But after that time, if your particular nucleus has not decayed, then there is a further 50% probability that it will decay after another half-life. Thus the total probability of decay is 0.5+0.5×0.5=0.750.5+0.5×0.5=0.75.
The reason for the extra factor of 0.5 in the second term is that your nucleus must not have decayed during the first half-life of your trial in order to decay sometime between one and two half-lives.
In simple language, after 2 half-lives (1/4)th fraction of nuclei will remain undecayed or (3/4)th fraction of nuclei will decay. Hence the probability that the nucleus decays in two half-lives is (3/4) =0.75
After every half-life of time, there is a 50% probability that any given nucleus will decay.
So after one-half-life, there is a 50% probability that a particular nucleus will have decayed. But after that time, if your particular nucleus has not decayed, then there is a further 50% probability that it will decay after another half-life. Thus the total probability of decay is 0.5+0.5×0.5=0.750.5+0.5×0.5=0.75.
The reason for the extra factor of 0.5 in the second term is that your nucleus must not have decayed during the first half-life of your trial in order to decay sometime between one and two half-lives.
In simple language, after 2 half-lives (1/4)th fraction of nuclei will remain undecayed or (3/4)th fraction of nuclei will decay. Hence the probability that the nucleus decays in two half-lives is (3/4) =0.75
