Chapter 28, Problem 5P

To determine

The minimum uncertainty in the energy of the state.

Answer to Problem 5P

The answer is $\text{6}{\text{.6×10}}^{\text{-8}}\text{eV}$

Explanation of Solution

Given info: Time is ${\text{10}}^{\text{-8}}\text{s}$

Formula used:

It is known that $\text{ΔE }\ge \frac{\text{h}}{\text{Δt}}$

Where,

  $h$ is Planck’s constant, $1.055\times {10}^{-34}J\cdot s$

  $\Delta \text{E}$ is uncertainty in Energy

  $\Delta \text{t}$ is time

Calculation:

Calculate the minimum uncertainty in the energy of the state by using the formula $\text{ΔE }\ge \frac{\text{h}}{\text{Δt}}$

  $\begin{array}{l}\text{=}\frac{\left(\text{1}{\text{.055×10}}^{\text{-34}}\text{J×s}\right)}{\left({\text{10}}^{\text{-8}}\text{s}\right)}\text{=1}{\text{.1×10}}^{\text{-26}}\text{J }\\ \text{= 6}{\text{.6×10}}^{\text{-8}}\text{eV}\end{array}$

Conclusion:

The required value is $\text{6}{\text{.6×10}}^{\text{-8}}\text{eV}$ .