n alpha particles per second are emitted from N atoms of a radioactive element. Then find the half life of radioactive element ?

Explanation

To find the half-life of a radioactive element when \( n \) alpha particles are emitted per second from \( N \) atoms, we can follow these steps:

### Step 1: Understand the decay process
The rate of decay of a radioactive substance is proportional to the number of undecayed nuclei present. This can be expressed mathematically as:
\[ \frac{dN}{dt} = -\lambda N \]
where:
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