Mean life of a radioactive sample is 100s . Then ,its half-life (in min) is

Options

A. 0.693
B. 1
C. `10^(-4)`
D. 1.155

Explanation

To find the half-life of a radioactive sample given its mean life, we can follow these steps:

### Step 1: Understand the relationship between mean life and decay constant
The mean life (τ) of a radioactive sample is related to the decay constant (λ) by the formula:
\[ \tau = \frac{1}{\lambda} \]
Given that the mean life (τ) is 100 seconds, we can express this relationship mathematically.

### Step 2: Calculate the decay constant (λ)
From the mean life formula, we can rearrange it to find λ:
\[ \lambda = \frac{1}{\tau} = \frac{1}{100 \text{ s}} = 0.01 \text{ s}^{-1} \]

### Step 3: Use the decay constant to find the half-life (T½)
The half-life (T½) is related to the decay constant by the formula:
\[ T_{1/2} = \frac{0.693}{\lambda} \]
Substituting the value of λ we found:
\[ T_{1/2} = \frac{0.693}{0.01} = 69.3 \text{ seconds} \]

### Step 4: Convert half-life from seconds to minutes
To convert the half-life from seconds to minutes, we divide by 60:
\[ T_{1/2} = \frac{69.3 \text{ s}}{60} \approx 1.155 \text{ minutes} \]

### Final Answer
The half-life of the radioactive sample is approximately **1.155 minutes**.

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