Question

A gamma ray photon has an energy of 0.91 GeV. (1 GeV = 109 eV.) What is the wavelength of the gamma ray in fm? (1 fm = 10-15 m)? Enter a number with 2 digits behind the decimal point.

Answer 1

Answer:

$\lambda=1.37 fm$

Explanation:

The Planck Eistein relation, states that the energy of a photon is proportional to its frequency:

$E=h\nu(1)$

h is the Plank constant.The frequency of a photon is defined as the speed of light over its wavelength:

$\nu=\frac{c}{\lambda}(2)$

Replacing (2) in (1):

$E=\frac{hc}{\lambda}\\\lambda=\frac{hc}{E}\\\lambda=\frac{(4.14*10^{-15}eV\cdot s)(3*10^8\frac{m}{s})}{0.91*10^{9}eV}\\\\\lambda=(1.37*10^{-15}m)*\frac{1fm}{10^{-15}m}\\\\\lambda=1.37 fm$