Answer
See answers.
Work Step by Step
The Compton wavelength for a particle of mass m is h/mc.
a. Find the Compton wavelength for an electron.
$$\frac{h}{m_e c} = \frac{6.626\times10^{-34}J\cdot s}{(9.11\times10^{-31}kg) (3.00\times10^8 m/s) }=2.43\times10^{-12}m$$
b. Find the Compton wavelength for a proton.
$$\frac{h}{m_p c} = \frac{6.626\times10^{-34}J\cdot s}{(1.67\times10^{-27}kg) (3.00\times10^8 m/s) }=1.32\times10^{-15}m$$
c. Use equation 27–4, E = hf, for the energy of a photon. The wavelength is the Compton wavelength.
$$E=hf=\frac{hc}{\lambda_C}$$
The Compton wavelength for a particle of mass m is h/mc.
$$E=\frac{hc}{h/mc}=mc^2$$
If a photon has a wavelength equal to a particle's Compton wavelength, the photon energy equals the particle's rest energy.
