Answer
The ratio of the wavelength of the photon to the wavelength of the electron is 100
Work Step by Step
We can find the wavelength of a photon with an energy of $0.100~keV$:
$E = \frac{hc}{\lambda_p}$
$\lambda_p = \frac{hc}{E}$
$\lambda_p = \frac{(6.626\times 10^{-34}~J~s)(3.0\times 10^8~m/s)}{(0.100\times 10^3~eV)(1.6\times 10^{-19}~J/eV)}$
$\lambda_p = 1.2424\times 10^{-8}~m$
We can find the wavelength of the electron:
$\lambda_e = \frac{h}{p_e}$
$\lambda_e = \frac{h}{\sqrt{2~m_e~E_e}}$
$\lambda_e = \frac{6.626\times 10^{-34}~J~s}{\sqrt{(2)(9.1\times 10^{-31}~kg)(100~eV)(1.6\times 10^{-19}~J/eV)}}$
$\lambda_e = 1.228\times 10^{-10}~m$
We can find the ratio of the wavelengths:
$\frac{\lambda_p}{\lambda_e} = \frac{1.2424\times 10^{-8}~m}{1.228\times 10^{-10}~m} = 100$
The ratio of the wavelength of the photon to the wavelength of the electron is 100.
