Write the relation between Half-Life and Mean-Life of radio active element.

Explanation

To establish the relation between the half-life (\( t_{1/2} \)) and the mean life (\( \tau \)) of a radioactive element, we can follow these steps:

### Step 1: Define Half-Life and Mean Life
- **Half-Life (\( t_{1/2} \))**: This is the time required for half of the radioactive nuclei in a sample to decay. It is a measure of the stability of the nucleus.
- **Mean Life (\( \tau \))**: This is the average time that a nucleus exists before it decays. It represents the expected lifetime of a radioactive particle.

### Step 2: Introduce the Decay Constant (\( \lambda \))
- The decay constant (\( \lambda \)) is a probability rate at which a nucleus decays. It is defined as the fraction of the remaining nuclei that decay per unit time.
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