Answer
16 GeV. $7.8\times10^{-17}m$.
Work Step by Step
The KE is 15 GeV, and the total energy is the sum of the kinetic energy and the proton’s mass energy.
$$E=KE+mc^2=15\times10^9 eV+938.3\times10^6 eV=16GeV$$
We find the relativistic momentum using equation 26-9.
$$p=\frac{\sqrt{E^2-(mc^2)^2}}{c}$$
Calculate the wavelength using the momentum.
$$\lambda=\frac{h}{p}=\frac{hc}{\sqrt{E^2-(mc^2)^2}}$$
$$\lambda=\frac{1240eV\cdot nm}{\sqrt{(15.938\times10^9 eV)^2-(938.3\times10^6 eV)^2 }}$$
$$\lambda=7.8\times10^{-8}nm=7.8\times10^{-17}m $$
