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 [2021]

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 [2021]

Smart Achievers · Accepted Answer

(4)

Out of 1000 nuclei of $Q$ , 60% may go $α$ -decay

i.e., 600 nuclei may have $α$ -decay

Decay constant

$t = 1 hour = 60 minutes$

From, $N = N_{0} e^{- λ i} = 600 \times e^{\frac{\ln 2}{20} \times 60}$

$∴$ $N = 75$

i.e., 75 nuclei are left after one hour.

So, number of nuclei decayed $= 600 - 75 = 525$

Solution

Q.
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 [2021]

1 50

2 75

3 350

4 525

Want Us to Email you About Special Offers & Updates?