Protactinium `""_(91)^(233)Pa` decays to `1/5`th of its initial quantitiy in 62.7 days. Calculate its decay constant and half-life.

Explanation

To solve the problem of calculating the decay constant and half-life of Protactinium \( _{91}^{233}Pa \), we will follow these steps:

### Step 1: Understand the given information
We know that Protactinium decays to \( \frac{1}{5} \) of its initial quantity in 62.7 days. This means:
- Initial quantity, \( N_0 \)
- Final quantity, \( N = \frac{N_0}{5} \)
- Time, \( t = 62.7 \) days

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