# Moseley Law

## Henry Moseley Law

After the experimental confirmation of Rutherford’s scattering theory in about the year 1913, the one-to-one relationship or link of an atom with its atomic number Z was proven by the work of Henry Moseley from the year 1887 to 1915.

Henry Moseley used the structure of Bohr’s atomic model to determine the energy radiated by an electron when it migrates from low-level orbitals. This energy released during migration has a strong dependence on an atomic number ‘Z’ so that by measuring the energy of the X-rays characteristic of any element, its atomic number Z can be confidently determined.

### Moseley Periodic Law

Here, we will measure the x-ray spectra of a number of elements and also identify several unknown elements by looking at their characteristics, viz: X-ray spectra.

Moseley’s law was discovered and published by an English Physicist named Henry Moseley. This law is an empirical law that concerns the characteristics of X-rays emitted by atoms.

The frequency v of X-ray emitted by an atom is related to its atomic number ‘Z’ by the following formula:

v = $\sqrt{(a-b)}$.....(1)

Here,

a and b = are constants. We also call these constants proportionality and screening or shielding constants.

Equation (1) is Moseley’s X-ray Carateristic formula and here the two physical constants ‘a’ and ‘b’ are independent constants of an element; however, these two depend on the X-ray series.

For a ‘k’ series, the value of a and b is:

a = $\sqrt{3RC/4}$ , and

b = 1

Where,

R = Rydberg’s constant

c = speed of light

For the L series, the value of a and b is as follows:

a = $\sqrt{5RC/36}$ , and

b  = 7.4

The relation between a and b is determined by experiments using Henry Moseley’s law and the graph for this relationship is as follows:

The line intersecting in the graph at the Z-axis shows that Z = b, where b is 1 for K series elements and 7.4 for elements in L series.

### Moseley Law Statement

A simple idea is that the effective charge of the nucleus decrements by 1 when it is being screened by an unpaired electron that persists behind in the K-shell. In any case, Bohr’s formula for Moseley’s K-alpha X-ray transitions is as follows:

E = hv

= E - E = $\frac{mq^{4}(Z-1)^{2}}{8h^{2}\varepsilon^{2}}$ ($\frac{1}{1^{2}}$ - $\frac{1}{2^{2}}$).....(2)

Now, dividing both the sides by ‘h’ and converting ‘E’ to ‘f’ in equation (2), we get:

f = v = ($\frac{3}{4}$) $\frac{mq^{4}(Z-1)^{2}}{8h^{2}\varepsilon^{2}}$ = (2.48 ∗ 10$^{15}$ Hz . (Z - 1)$^{2}$).....(3)

Here, one must know that equation (3) is the Moseley equation.

### Moseley X-Ray Experiment

X-ray spectrometers are the fundamental foundation-stones of the process of X-ray crystallography.

The working by Moseley by employing X-ray spectrometers is as follows:

A glass-bulb electron tube was used, inside this evacuated tube, electrons were fired at a metallic substance, which was a sample of the pure element in his work.

The firing of electrons on a metallic substance caused the ionization of electrons from the inner electron shells of the element. The rebound of electrons into the holes in the inner shells then caused the emission of X-ray photons leaving out the tube in a semi-beam, through an opening in the external X-ray shielding.

Now, these radiated X-rays were then diffracted by a standardized salt crystal, with angular results emitting in the form of photographic lines by the exposure of an X-ray film fixed at the outside the vacuum tube at a known distance.

Next, Moseley employed the application of Bragg's law after initial guesswork of the mean distances between atoms in the metallic crystal, based on its density next leading to calculate the wavelength of the emitted X-rays.

### Analysis of Moseley’s Experiment

To Determine the following things:

• Firstly, we must confirm Moseley’s law with six known samples of elements. Since the energy is the characteristic X-ray (according to Moseley), which is proportional to (Z - n)$^{2}$ and channel number N is directly proportional to E, then N is proportional to (Z - n)$^{2}$. Therefore, N kZ = − bg n.

• Draw a graph plotting N vs. Z for the six known samples. Obtain the best values of k and n can be observed from this graph. Now, look at your spectra carefully and think about what the uncertainties in your data are. Devise a reasonable method for determining the uncertainties in n and k.

• Determine Z for the unknowns by comparing the peak position for each with your results from the six known samples and also determine the uncertainty associated with your findings.

So, this is how we can determine the atomic number of a material; by observing the X-ray characteristic of an element.

Question 1: What is the Basic Idea of Moseley’s Law?

Answer: Photographic recording of Kα and Kβ x-ray emission lines for a range of varying elements can be determined by using Moseley’s law; we must note that for the dispersive element, the line position is proportional to the wavelength. Here, Moseley’s law concerns the characteristic X-rays emitted by various atoms.

Question 2: What is Periodic Law?

Answer: This law states that all the elements in a periodic table are arranged in increasing order where each element has its own physical and chemical property.

Question 3: How Moseley’s Law Influences Physics?

Answer: The development of Moseley's law in X-ray spectra has led to the introduction of advanced atomic physics, nuclear physics, and quantum physics by providing the first experimental evidence in favour of Niels Bohr's theory, apart from the hydrogen atom spectrum that the Bohr theory was designed through.

Question 4: What is Moseley’s Empirical Formula?

Answer: Moseley's empirical formula for Kα X-rays were adapted to the Bohr model. The implication of the relationship between these two models is that the single electron in the K-shell before the emission is about 100% effective in shielding the nucleus so that the electron from the L-shell obtains an effective nuclear charge of Z-1.