Q. 22

# What are the dimensions of χ, the magnetic susceptibility? Consider an H-atom. Guess an expression for χ, up to a constant by constructing a quantity of dimensions of χ, out of parameters of the atom: e, m, v, R and μ_{0}. Here, m is the electronic mass, v is electronic velocity, R is Bohr radius. Estimate the number so obtained and compare with the value of _{} for many solid materials.

Answer :

is magnetic susceptibility and it is the property of the substance which shows how easily it can be magnetized.

It can also be defined as the ratio of Intensity of magnetization (I) in a substance to the magnetic intensity applied to the substance (H)

Hence,

Here, I and H have the same units and hence is dimensionless.

Dimensions of

Dimensions of … electric charge

] =

Question says to use and e. The possible combination is .

Upon comparing the powers of respective Fundamental Unit we get the following equations

For M

… (1)

For L

… (2)

For T

… (3)

For A

… (4)

From (1), (2) and (3)

Hence,

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