X-Ray Spectroscopy: Calculating Wavelength & Angle

[Scarpetta]

An x-ray photon has a characteristic energy of 2.320keV. Determine its equivalent wavelenth in nm and the angle at which you would set a WD spectrometer containing an ADP dispersing crystal with an effective d spacing of 10.64A.

I would appreciate any help on this question please, i don't expect to be given the answers but if some one could show some example calcs or tell me where i can find some i would be very grateful, I've been on the web all day and not had any luck, please help!

Thanks

Scarpetta

 

[Valerie Park]

Wavelength in nm: The energy of an x-ray photon can be converted to its equivalent wavelength in nm using the equation E = hc/λ, where h is Planck's constant (6.626 × 10^-34 J s), c is the speed of light (2.998 x 10^8 m/s) and λ is the wavelength in nm. E = (6.626 x 10^-34 J s)(2.998 x 10^8 m/s)/λ λ = (6.626 x 10^-34 J s)(2.998 x 10^8 m/s)/2.320keV λ = 535.24 nm Angle at which you would set the WD spectrometer: The angle at which you would set a WD spectrometer containing an ADP dispersing crystal with an effective d spacing of 10.64A can be determined using the equation θ = 2Δ/λ, where Δ is the effective d spacing of the crystal (10.64A) and λ is the wavelength of the x-ray photon (535.24nm). θ = 2(10.64A)/535.24nm θ = 0.0553 rad = 3.19°

 

[sir-pinski]

To calculate the wavelength of the x-ray photon with an energy of 2.320keV, we can use the equation E = hc/λ, where E is the energy, h is Planck's constant (6.626 x 10^-34 J*s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength.

First, we need to convert the energy from keV to Joules by multiplying by 1.602 x 10^-16. So, 2.320keV is equivalent to 3.718 x 10^-16 J.

Next, we can plug in the values into the equation to solve for the wavelength:

3.718 x 10^-16 J = (6.626 x 10^-34 J*s)(3.00 x 10^8 m/s)/λ

Rearranging the equation to solve for λ, we get:

λ = (6.626 x 10^-34 J*s)(3.00 x 10^8 m/s)/3.718 x 10^-16 J

λ = 1.34 x 10^-10 m

Finally, we can convert this to nanometers by multiplying by 10^9, giving us a wavelength of 134nm for the x-ray photon.

To determine the angle at which we would set a WD spectrometer containing an ADP dispersing crystal with an effective d spacing of 10.64A, we can use the Bragg's Law equation, nλ = 2dsinθ, where n is the order of diffraction, λ is the wavelength, d is the distance between crystal planes, and θ is the angle of incidence.

In this case, n = 1 (first order diffraction), λ = 1.34 x 10^-10 m (calculated above), d = 10.64A = 10.64 x 10^-10 m.

Plugging in the values, we get:

1.34 x 10^-10 m = 2(10.64 x 10^-10 m)sinθ

Solving for θ, we get:

θ = sin^-1(1.34 x 10^-10 m/2(10.64 x 10^-10 m))

θ = 6.31°

Therefore, the angle at which we would set the WD spectrometer is