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!
To find the energy of the gamma-ray photon, we can use the equation for the conservation of energy:
E_photon = E_electron + E_positron
Given that each particle has a kinetic energy of 275 keV, we convert this to MeV:
E_particle = 275 keV = 275 * 10^-6 MeV = 0.275 MeV
Therefore, the energy of the gamma-ray photon is:
E_photon = 2 * E_particle = 2 * 0.275 MeV = 0.55 MeV
So, the energy of the photon is 0.55 MeV.
To find the wavelength of the photon, we can use the equation for the energy of a photon:
E_photon = hc / λ
Where:
E_photon is the energy of the photon,
h is Planck's constant (6.626 × 10^-34 J*s),
c is the speed of light (3 × 10^8 m/s),
and λ is the wavelength of the photon.
Let's convert the energy of the photon from MeV to joules:
E_photon = 0.55 MeV = 0.55 * 1.6 × 10^-13 J = 8.8 × 10^-14 J
Now, we rearrange the equation to solve for the wavelength:
λ = hc / E_photon
Substituting the values:
λ = (6.626 × 10^-34 J*s * 3 × 10^8 m/s) / (8.8 × 10^-14 J)
Calculating:
λ ≈ 2.25 × 10^-6 m
Therefore, the wavelength of the photon is approximately 2.25 × 10^-6 meters.
To determine the energy of the gamma-ray photon, we can use the principle of conservation of energy. We know that the energy of the produced electron and positron pair is 275 keV each. Since the pair was generated from the photon, the total energy of the electron-positron pair is equal to the energy of the photon.
Step 1: Convert the kinetic energy of each particle to MeV:
275 keV = 0.275 MeV
Step 2: Add the energies of the electron and positron:
Total energy of the electron-positron pair = 0.275 MeV + 0.275 MeV = 0.55 MeV
Therefore, the energy of the gamma-ray photon that produced the electron-positron pair is 0.55 MeV.
To determine the wavelength of the photon, we can use the wave-particle duality of light. The energy of the photon is related to its wavelength by the equation:
Energy (E) = Planck's constant (h) * Speed of light (c) / Wavelength (λ)
Step 1: Convert the energy of the photon to joules:
Energy of the photon = 0.55 MeV = 0.55 * 1.6 x 10^-13 J = 8.8 x 10^-14 J
Step 2: Substitute the values into the equation and solve for the wavelength:
Wavelength (λ) = Planck's constant (h) * Speed of light (c) / Energy (E)
λ = (6.626 x 10^-34 J.s) * (3 x 10^8 m/s) / (8.8 x 10^-14 J)
λ ≈ 2.39 x 10^-12 m
Therefore, the wavelength of the gamma-ray photon is approximately 2.39 x 10^-12 meters.