K alpha and K beta wavelengths

[Mrbilly]

Homework Statement

Calculate the Kα and Kβ wavelengths for He and Li
Ive seen https://www.physicsforums.com/showthread.php?t=118050 and the two websites that were given for tables, but I need to show calculations.

Homework Equations

K alpha Energy=10.2eV*(Z-1)²?

E=hc/λ

The Attempt at a Solution

Ive tried using the above equations to find energy and thus wavelengths for He and Li k-alpha, but they don't match the values found from http://xdb.lbl.gov/Section1/Table_1-2.pdf and http://www.csrri.iit.edu/periodic-table.html says they have no wavelengths... I also have no idea how to calculate for k beta.

 

[anathema]

Can someone please help me out?

First, let's clarify the equations for calculating Kα and Kβ wavelengths. The Kα and Kβ wavelengths for a given element can be calculated using the following equations:

Kα wavelength: λ = hc/(E_Kα - E_K)
Kβ wavelength: λ = hc/(E_Kβ - E_K)

Where:
hc = Planck's constant (6.626 x 10^-34 J*s) multiplied by the speed of light (3.00 x 10^8 m/s)
E_Kα = Energy of the Kα transition
E_Kβ = Energy of the Kβ transition
E_K = Energy of the K shell (for He and Li, this is 1s)

To find the energy of the Kα and Kβ transitions for He and Li, we can use the following equations:

Energy of Kα transition: E_Kα = 10.2 eV * (Z-1)^2
Energy of Kβ transition: E_Kβ = 10.2 eV * (Z-2)^2

Where:
Z = atomic number of the element (2 for He, 3 for Li)

Plugging in the values for He, we get:
Energy of Kα transition: E_Kα = 10.2 eV * (2-1)^2 = 10.2 eV
Energy of Kβ transition: E_Kβ = 10.2 eV * (2-2)^2 = 0 eV

Therefore, the Kα wavelength for He is:
λ = hc/(E_Kα - E_K) = (6.626 x 10^-34 J*s * 3.00 x 10^8 m/s) / (10.2 eV - 0 eV) = 6.199 x 10^-11 m

For Li, we get:
Energy of Kα transition: E_Kα = 10.2 eV * (3-1)^2 = 40.8 eV
Energy of Kβ transition: E_Kβ = 10.2 eV * (3-2)^2 = 10.2 eV

Therefore, the Kα wavelength for Li is:
λ = hc/(E_Kα - E_K) = (6.626 x 10^-34 J*s * 3.00 x 10^8 m/s)