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

Options

A. 50
B. 75
C. 350
D. 525

Explanation

To solve the problem of finding the number of alpha decays of nucleus Q in the first hour, we can follow these steps:

### Step 1: Understand the Given Information
- Half-life of nucleus Q, \( T_{1/2} = 20 \) minutes.
- Initial number of nuclei, \( N_0 = 1000 \).
- Probability of alpha decay, \( P_{\alpha} = 60\% = 0.6 \).
- Probability of beta decay, \( P_{\beta} = 40\% = 0.4 \).
- Total time, \( T = 1 \) hour = 60 minutes.
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