Question

The p⁰ is a subatomic particle of fleeting existence. Data tables don't usually quote its lifetime. Rather, they quote a "width," meaning energy uncertainty, of about 150MeV. Roughly what is its lifetime?

Short answer

The lifetime is $∆t⩾2.2\times {10}^{-24}sec$.

Step-by-step solution

Given data.

Energy $∆E=150MeV$.

Uncertainty principle for energy and time.

$∆t∆E⩾\frac{h}{2}$

Energy value,

$\begin{array}{rcl}∆E& =& 150MeV\\ & =& 150\times {10}^6\times 1.6\times {10}^{-19}J\\ & =& 240\times {10}^{-13}J\end{array}$

So,

$$\begin{gathered} ∆t⩾\frac{1.05\times {10}^{-34}}{240\times {10}^{-13}} \\ ∆t⩾2.2\times {10}^{-24}sec \end{gathered}$$

Therefore, a lifetime is required$∆t⩾2.2\times {10}^{-24}sec$.