Chapter 32, Problem 28P

To determine

The uncertainty in rest energy of $\Sigma °$ particle if the mean life is $7\times {10}^{-20}s$ express in MeV?

Answer to Problem 28P

Solution:

The uncertainty in rest of energy of the particle is $9.4\times {10}^{-3}MeV$.

Explanation of Solution

Given info.:

The mean life $\left(\Delta t\right)$ of $\Sigma °$ particle is $7\times {10}^{-20}s$.

Formula used:

Heisenberg’s uncertainty principle can be expressed as

$\Delta E=\frac{h}{2\pi \Delta t}$

Here,

h: Planck’s constant.

$\Delta t$: Uncertainty in time.

Calculation:

Substitute $6.63\times {10}^{-34}J-s$ for h, $\Delta t=7\times {10}^{-20}s$

$\Delta E=\frac{6.63\times {10}^{-34}J-s}{2\pi \times \left(7\times {10}^{-20}s\right)}$

$\begin{array}{l}=1.51\times {10}^{-15}J\\ =1.51\times {10}^{-15}J\times \frac{1MeV}{1.6\times {10}^{-13}J}\\ =9.4\times {10}^{-3}MeV\end{array}$

Therefore, the uncertainty in rest energy of the particle is $9.4\times {10}^{-3}MeV$.