The number of `alpha`-particles emitted per second by 1g of radium is `3.608 xx 10^(10)`. Calculate decay constant and `t_((1)/(2))`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the relationship between the decay constant and activity
The activity (A) of a radioactive substance is given by the formula:
\[ A = -\frac{dN}{dt} = \lambda N \]
where:
- \( A \) is the activity (number of decays per second),
- \( \lambda \) is the decay constant,
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