find the energy of an x-ray photon which can impact a maximum energy of 50 kev to an electron
Find the energy of x _ray photon which can impart a maximum energy of 50 Kev to an electron.
KE = h(nu_i - nu_f) but for maximum transfer of energy nu_f = 0.5*nu_i.
So answer will be 100 keV.
To find the energy of an X-ray photon that can impact a maximum energy of 50 keV to an electron, you can use the equation for the energy of a photon:
E = hf
Where:
E is the energy of the photon
h is Planck's constant (6.626 x 10^-34 J·s)
f is the frequency of the photon
First, we need to convert the maximum energy of 50 keV to joules.
1 keV = 1.602 x 10^-16 J
50 keV = 50 x 1.602 x 10^-16 J = 8.01 x 10^-15 J
Since the photon is impacting the electron with this maximum energy, the energy of the photon must be equal to that. Therefore:
E = 8.01 x 10^-15 J
Next, we can rearrange the equation to solve for the frequency of the photon:
f = E / h
Substituting the known values:
f = (8.01 x 10^-15 J) / (6.626 x 10^-34 J·s)
Calculating:
f ≈ 1.210 x 10^19 Hz
Now, we can substitute this frequency into the equation to find the energy of the X-ray photon:
E = (1.210 x 10^19 Hz) × (6.626 x 10^-34 J·s)
Calculating:
E ≈ 8.01 x 10^-15 J
Therefore, the energy of the X-ray photon that can impact a maximum energy of 50 keV to an electron is approximately 8.01 x 10^-15 J.
To find the energy of an x-ray photon, we can use the equation:
E = hc / λ,
where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3 x 10^8 m/s), and λ is the wavelength of the photon.
Since we are given the maximum energy of the x-ray photon, we need to convert 50 keV to joules. 1 keV is equal to 1.602 x 10^-16 J. So, 50 keV will be:
E = (50 x 1.602 x 10^-16 J) = 8.01 x 10^-15 J.
Now, we can find the wavelength of the photon using the following equation:
λ = hc / E.
Plugging in the values, we have:
λ = (6.626 x 10^-34 J·s * 3 x 10^8 m/s) / (8.01 x 10^-15 J).
Simplifying, we get:
λ = 2.472 x 10^-10 m.
Therefore, the wavelength of the x-ray photon that can impact a maximum energy of 50 keV is approximately 2.472 x 10^-10 m.