Question

In Moseley’s equation \[\sqrt v = a\left( {Z - b} \right)\]
A.b depends on metal and a is independent of metal
B.both a and b are metal dependent
C.both a and b are independent of metal
D.a is metal dependent while b is not

Answer 1

Hint: Moseley’s law is derived from Bohr’s atomic theory. And hence similar to the atomic theory of Bohr, it also deals with the frequency of the x rays emitted by the atoms under study. It also manages to establish a relationship between the atomic number and the corresponding x-ray frequency of the atom.

Complete step by step answer:
Moseley’s Law is related to the characteristic X – rays that are emitted by atoms. Let us first understand the need for Moseley’s law.
The historic period was designed to place elements in the increasing order of their atomic masses. This system worked fine until they found some anomalies in such a system. Some elements having higher atomic weights were placed before the element with a lower atomic weight. This was done because the chemical characteristics as well as physical characteristics suggested that the heavier element must be placed before the lighter ones.
Henry Moseley was a scientist who found that this system is flawed and wanted to bring out a uniformity while arranging the element in the periodic table. Moseley studied the characteristic X – rays of the various elements that were discovered till then. He rearranged the element in the periodic table atomic to the results obtained from these x - ray characteristics. He then stated that the basis of this rearrangement was a property he termed to be the atomic number of the element. He characterised this property on the basis of the equation: \[\sqrt v = a\left( {Z - b} \right)\] .
In this equation, v represents the frequency of the x ray while Z represents the atomic number. Also, a and b are constant values which depend on the particular spectral line and hence they are independent of the metal used.

Hence, Option C is the correct option.

Note:
Moseley's formula, not only established atomic number as a measurable experimental quantity but gave it a physical meaning as the positive charge on the atomic nucleus.