Chapter 27, Problem 34P

To determine

The longest wavelength photon that can produce a proton- antiproton pair.

Answer to Problem 34P

Solution:

The photon’s longest wavelength that can produce a proton- antiproton pair is $6.62\times {10}^{-16}\text{m}$.

Explanation of Solution

Given:

Mass of the proton & antiproton: $1.67\times {10}^{-27}\text{kg}$

Formula Used:

$hf=\frac{hc}{\lambda }=2m_0{c}^2$

Where, h = Plank’s Constant

$c$= velocity of light

$\lambda$ =wavelength

Calculation:

Mass of each proton and antiproton: $1.67\times {10}^{-27}\text{kg}$

The longest wavelength photon will have minimum energy to produce a proton-antiproton pair as,

$\begin{array}{c}h{f}_{\min }=\frac{hc}{{\lambda }_{\max }}=2m_0{c}^2\\ \text{so,}\frac{hc}{{\lambda }_{\max }}=2m_0{c}^2\\ \frac{6.63\times {10}^{-34}\text{J}\text{s}}{{\lambda }_{\max }}=2(1.67\times {10}^{-27}\text{kg})(3\times {10}^8\text{m/s})\\ {\lambda }_{\max }=\frac{6.63\times {10}^{-34}\text{J}\text{s}}{2(1.67\times {10}^{-27}\text{kg})(3\times {10}^8\text{m/s})}\\ {\lambda }_{\max }=6.62\times {10}^{-16}\text{m}\end{array}$