The duration of a laser pulse is `10^(-8)` s. The uncertainly in its energy will be

Options

A. `6.6xx10^(-26)`J
B. `6.6xx10^(-42)` J
C. `6.6xx10^(-34)` J
D. `1/6.6xx10^26` J

Answer

To find the uncertainty in energy (ΔE) of a laser pulse with a duration of \(10^{-8}\) seconds, we will use Heisenberg's uncertainty principle, which states:

\[ \Delta E \cdot \Delta t \geq h \]

where:
- \(\Delta E\) is the uncertainty in energy,
- \(\Delta t\) is the uncertainty in time (duration of the pulse),
- \(h\) is Planck's constant, approximately \(6.63 \times 10^{-34} \, \text{J s}\).

### Step-by-Step Solution:

1. **Identify Given Values**:
- Duration of the laser pulse, \(\Delta t = 10^{-8} \, \text{s}\).
- Planck's constant, \(h = 6.63 \times 10^{-34} \, \text{J s}\).

2. **Apply Heisenberg's Uncertainty Principle**:
According to the principle, we can rearrange the formula to find the uncertainty in energy:
\[ \Delta E \geq \frac{h}{\Delta t} \]

3. **Substitute the Values**:
Substitute the known values of \(h\) and \(\Delta t\) into the equation:
\[ \Delta E \geq \frac{6.63 \times 10^{-34} \, \text{J s}}{10^{-8} \, \text{s}} \]

4. **Perform the Calculation**:
Calculate \(\Delta E\):
\[ \Delta E \geq 6.63 \times 10^{-34} \div 10^{-8} = 6.63 \times 10^{-26} \, \text{J} \]

5. **Conclusion**:
The uncertainty in the energy of the laser pulse is:
\[ \Delta E \geq 6.63 \times 10^{-26} \, \text{J} \]

### Final Answer:
The uncertainty in the energy of the laser pulse is approximately \(6.63 \times 10^{-26} \, \text{J}\).

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