Question

Here are the${\mathbf{K}}_{\mathbf{\alpha }}$ wavelengths of a few elements:

Element	λ(pm)	Element	λ(pm)
Ti	275	Co	179
V	250	Ni	166
Cr	229	Cu	154
Mn	210	Zn	143
Fe	193	Ga	134

Make a Moseley plot (like that in Fig. 40-16) from these data and verify that its slope agrees with the value given for C in Module 40-6.

Short answer

The slope of the Moseley plot is calculated using the given data and it is verified that the slope of the graph agrees with the values given for C.

Step-by-step solution

The given data

The${\mathrm{K}}_{\mathrm{\alpha }}$ wavelengths of a few elements are given in the table.

 Step 2: Understanding the concept of wavelength and Moseley plot:

Using the given data in the table of the wavelengths of the different elements, we can get the graph of a Moseley plot. Now using the basic slope formula, we can get the slope of the given graph to verify the values in the given table.

Formula:

The slope of a graph,

$\mathrm{m}=\frac{{\mathrm{y}}_2-{\mathrm{y}}_1}{{\mathrm{x}}_2-{\mathrm{x}}_1}$ ….. (1)

Calculation for the slope of the Moseley plot:

From the given data in the table, the frequencies of the square roots are calculated and their square roots are taken by comparing the atomic numbers and the dong the least-square fit, and define the slope of the plot.

The least squares procedure also returns a value for the y-intercept of this statistically determined “best-fit“line; that result is negative and would appear on a graph like a Figure to be about on the vertical axis.

Also, the slope of the plot is found using equation (1) as:

$\frac{\left(1.95-0.50\right){10}^9{\mathrm{Hz}}^{1/2}}{40-11}=5\times {10}^7{\mathrm{Hz}}^{1/2}$

Thus, the result (or the slope) is$5.02\times {10}^7$ with the odd-sounding unit of a square root of a hertz and it is verified that the slope of the graph agrees with the values given for C.