2. (16 points) (a) Write down an equation similar to Moseley\'s law for La x-ray

Question

2. (16 points) (a) Write down an equation similar to Moseley's law for La x-rays, which involve transi- tions from n 3ton 2. Assuming screening of the nuclear charge by all electrons in the K and L shells is perfect, what would be the slope and -intercept of a Moseley plot similar to Fig. 8.16? b) Using software of your choice (Excel, Google Sheets, plotly,.., draw a Moseley plot for La x-rays using the following energies in keV: Mn 0.721, Zn 1.11, Br 1.60, Zr 2.06, Rh 2.89, Sn 3.71, Cs 4.65, Nd 5.72 Fit the data to a line, provide the slope and r-intercept, and compare with the results of part (a) 150 Slope - 3.22 100 50 Intercept-1 0 0 10 20 30 40 50 60 Atomic number Z FIGURE 8.16 Moseley plot of square root of Ka X-ray energy as a function of atomic number.

Explanation / Answer

solution:

moseley's law

a. sqroot(f) = k1.(Z - k2)

for Lalpha line, asuming screening of nuclear charges by K, L shells is perfect

then

k2 = 2

and

the formula becomes

f = (5/36)*(3.29*10^15)(Z - 2)^2

f = 4.56944*10^14(Z - 2)^2

now, dE = h*f

sqroot(dE) = sqroot(h*f) = sqroot(h*4.56944*10^14)(Z - 2)

hence

h = 6.63*10^-34/1.6*10^-19 ( in units of electron volts)

hence

sqroot(dE) = 1.37499Z - 2.7499

so slope is 1.37499

intercept is -2.7499

b. for the given Lalpha energies

Element Atomic NUmber E

Mn 25 0.721 keV

Zn 30 1.11

Br 35 1.6

Zr 40 2.06

Rh 45 2.89

Sn 50 3.71

Cs 55 4.65

Nd 60 5.72

plotting this (sqrt(E)) vs Z on excel we get

sqrt(E) = 0.0442Z - 0.281

we can see the slop obtained form this method is different from the slop obtained by previous method and so os the intercept

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