A gamma-ray photon produces an electron-positron pair, each with a kinetic energy of 275keV .
What was the energy of the photon?
E=in MeV
What was the wavelength of the photon?
wavelength in m
Please help thank you!
i am not sure
To determine the energy of the gamma-ray photon, you can use the equation E = mc^2, where E is the energy, m is the mass, and c is the speed of light.
In this case, the gamma-ray photon produces an electron-positron pair, so the mass of an electron and positron should be considered.
The rest mass energy of an electron is approximately 0.511 MeV/c^2. Therefore, the total mass energy of the electron-positron pair would be twice that, i.e., 2 * 0.511 MeV = 1.022 MeV.
Since the gamma-ray photon completely converts its energy into mass energy, the energy of the photon should be equal to the energy of the electron-positron pair. Therefore, the energy of the photon is 1.022 MeV.
To find the wavelength of the photon, you can use the equation λ = c / f, where λ is the wavelength, c is the speed of light, and f is the frequency of the wave.
The energy of a photon can also be related to its frequency using the equation E = hf, where E is the energy, h is Planck's constant (approximately 4.1357 × 10^-15 eV*s), and f is the frequency.
Using these two equations, you can derive the equation λ = c / (E / h).
Substituting the values, we get:
λ = (2.998 × 10^8 m/s) / (1.022 MeV / (4.1357 × 10^-15 eV*s))
Note that the energy needs to be converted from MeV to eV.
Simplifying the equation, we find the wavelength of the photon.
Remember to convert the wavelength to meters by dividing by 10^9 since the wavelength is usually measured in nanometers (nm).
I hope this helps!