Chapter 32, Problem 34P

To determine

The expected lifetime of the virtual W particle.

Answer to Problem 34P

Solution: The expected lifetime of the virtual W particle is $8\times {10}^{-27}\text{s}$ .

Explanation of Solution

Given info: The mass of the decaying particle is less than the mass of the virtual W particle.

Formula to calculate the expected lifetime of the radioactive decay particle using uncertainty principle is,

  $\begin{array}{c}\Delta E\cdot \Delta t=\frac{h}{2\pi }\\ \Delta t=\frac{h}{2\pi \Delta E}\end{array}$

• $\Delta E$ is the energy width of lifetime.
• $\Delta t$ is the expected time.
• $h$ is the Planck’s constant.

Substitute $6.64\times {10}^{-34}\text{J}\cdot \text{s}$ for $h$ and $80.385\times {10}^9\text{eV}$ for $\Delta E$ .

  $\begin{array}{c}\Delta t=\frac{6.64\times {10}^{-34}\text{J}\cdot \text{s}}{2\times 3.14\times 80.385\times {10}^9\text{eV}\times \frac{1.6\times {10}^{-19}\text{J}}{1\text{eV}}}\\ =8\times {10}^{-27}\text{s}\end{array}$

Conclusion: Therefore, the expected lifetime of the virtual W particle is $8\times {10}^{-27}\text{s}$ .