A free neutron has half life of 14 minutes. Its decay constant is

Options

A. `8.25xx10^(-2) S^(-1)`
B. `8.25xx10^(-3) S^(-1)`
C. `8.25xx10^(-4) S^(-1)`
D. `8.25xx10^1 S^(-1)`

Answer

To find the decay constant (\(\lambda\)) of a free neutron with a half-life of 14 minutes, we can use the following steps:

### Step 1: Convert Half-Life to Seconds
The half-life (\(t_{1/2}\)) of the neutron is given as 14 minutes. We need to convert this time into seconds because the decay constant is typically expressed in seconds inverse (s\(^{-1}\)).

\[ t_{1/2} = 14 \text{ minutes} \times 60 \text{ seconds/minute} = 840 \text{ seconds} \]

### Step 2: Use the Decay Constant Formula
The decay constant (\(\lambda\)) is related to the half-life by the formula:

\[ \lambda = \frac{0.693}{t_{1/2}} \]

### Step 3: Substitute the Half-Life Value
Now, we can substitute the value of \(t_{1/2}\) we calculated in Step 1 into the formula:

\[ \lambda = \frac{0.693}{840 \text{ seconds}} \]

### Step 4: Calculate the Decay Constant
Now we perform the calculation:

\[ \lambda = \frac{0.693}{840} \approx 8.25 \times 10^{-4} \text{ s}^{-1} \]

### Final Answer
Thus, the decay constant (\(\lambda\)) for a free neutron with a half-life of 14 minutes is approximately:

\[ \lambda \approx 8.25 \times 10^{-4} \text{ s}^{-1} \]

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