A laser produces a beam of $4000 - \mathrm { nm }$ light. A shutter allows a pulse of light, $30 \mathrm { ps }$ in duration, to pass through. What is the uncertainty in the energy of a photon in the pulse? $\left( 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} \right.$, $h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s }$ )

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Quizplus · Accepted Answer

The uncertainty in energy can be calculated using the energy-time uncertainty principle: $\Delta E \Delta t \geq \frac{h}{4\pi}$. Given $\Delta t = 30 \, \text{ps} = 30 \times 10^{-12} \, \text{s}$, we find $\Delta E \geq \frac{6.626 \times 10^{-34}}{4\pi \times 30 \times 10^{-12}}$. Converting this result to eV gives approximately $2 \times 10^{-5} \, \text{eV}$.

A Laser Produces a Beam Of 4000−nm4000 - \mathrm { nm }4000−nm

A Laser Produces a Beam Of $4000 - \mathrm { nm }$