consider an x-ray tube with a Cun anode and a monochromator consisting of a Ni single crystal with (111) planes parallel to surface of crystal. what is the lowest voltage capable of producing X-rays trough a monochromator ?
answer in V.
To determine the lowest voltage capable of producing X-rays through a monochromator, you need to calculate the binding energy of the Ni (111) crystal planes.
The binding energy can be calculated using the equation:
E = (h^2 * n^2) / (8 * m * d^2)
Where:
E is the binding energy
h is the Planck's constant
n is the principal quantum number (in this case, it corresponds to the Miller indices, which is 111)
m is the reduced mass of an electron and a Ni atom
d is the distance between consecutive (111) crystal planes
The value of the reduced mass (m) is calculated as the product of the electron mass and the Ni atomic mass, divided by their sum.
Now, the binding energy corresponds to the energy difference between the electron energy levels in the Ni crystal, which is given by the equation:
E = (e * V) / N
Where:
e is the elementary charge
V is the voltage applied to the crystal
N is the number of atoms in the crystal
We can rearrange the equations to solve for V:
V = (E * N) / e
To find the lowest voltage, we need to find the smallest value of binding energy (E). This corresponds to the maximum value of the voltage (V).
So, to find the lowest voltage capable of producing X-rays through the monochromator, you need information on the binding energy (E) and the number of atoms (N) in the crystal. With these values, you can calculate the voltage (V) using the equation above.