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 =(a−b)−−−−−− \[\sqrt{(a-b)}\]        .....(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 Characteristic 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 = \[\frac{3RC}{4}\]−−−−−−\[\sqrt{\frac{3RC}{4}}\]

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 = \[\frac{5RC}{36}\]—-------- \[\sqrt{\frac{5RC}{36}}\],

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 decreases by 1 when it is being screened by an unpaired electron that persists behind in the K-shell.

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 and channel number N is directly proportional to E, then N is proportional to (Z - n). Therefore, N kZ = − bg n. 

• Draw a graph plotting N vs. Z for the six known samples. Obtaining 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. 

Moseley’s Law and a Basic Introduction

Moseley’s law is used to understand the emitted x-rays by the atoms. This law was derived and published by Henry Moseley. He used this law to determine the energy exerted by an atom. Atoms are the smallest particle that exists. And to find the energy that is exerted by the atom, Moseley’s law is used. It is an empirical law that determines the atomic number. 

Students can find more information about Moseley’s law on the Vedantu website. It has all free downloadable content that students can use and study. It is important to practice all the formulas with example questions to get a better understanding of the law. This law is very important as it created the basis of the periodic table and also helped in discovering new elements that were previously unknown to the scientists. 

Statement of the Moseley’s Law

The statement of moseley’s law is: “The square root of the frequency of the x-ray emitted by an atom is proportional to its atomic number”. New elements were also found because of this law. This law came to existence because when Henry Moseley was studying graphs, he found a strange relationship between the lines and the atomic number. This law also helped with organizing the elements on the periodic table based on atomic numbers rather than atomic mass. 

The formula for Moseley’s law is ν=a(Z–b)…(1) 

Importance of Moseley’s law 

Moseley’s law is very important because it proved that atomic numbers are more necessary than atomic mass and it is because of this reason that the entire periodic table was changed based on the element's atomic number. This law also helped with discovering new elements and explained the property of elements way better. 

In 1914, Moseley also published a paper where he spoke about three unknown elements between two others and because of all his experiments and data, we now have more information about how to study elements. He also found that the K lines were related to the atomic number and later found the formula by which the approximated relationship between them could be calculated. 

The formula which is called Moseley’s Law is: 

V = A . (Z – b)²

In this case, 

• V is the frequency of the x-ray emitted line

• A and b are constants that depend on the type of notation