Question 67: Atoms & Nuclei

Question

A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decays of Q in the first one hour is

Accepted Answer

Out of 1000 nuclei of Q, 60% may go $$\alpha$$-decay
$$\Rightarrow$$ 600 nuclei may have $$\alpha$$-decay
$$\lambda  = {{\ln 2} \over {{t_{1/2}}}} = {{\ln 2} \over {20}}$$
t = 1 h = 60 min
Using,
$$N = {N_0}{e^{ - \lambda t}} = 600 	imes {e^{ - {{\ln 2} \over {20}} 	imes 60}}$$
N = 75
$$\Rightarrow$$  75 nuclei are left after one hour
So, number of nuclei decayed = 600 $$-$$ 75 = 525

Answer

50

Answer

75

Answer

350

Answer

525

Atoms & Nuclei

A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decays of Q in the first one hour is

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