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A domain if ferromagnetic iron is in the...

A domain if ferromagnetic iron is in the form of cube of side length `1mum`. Estimate the number of iron atoms in the domain and the maximum possible moment and magnetisation of the domain. The molecular mass iron is 55 g/mol and its density is `7.9g//cm^3` . Assume that each iron atom has a dipole moment of `9.27xx10^(-24) Am^2`.

Text Solution

Verified by Experts

The volume of the cubic domain is V = `(10^(-6)m) ^3=10^(-18)=10^(-12)cm^3`
Its mass is volume `xx` density `=7.9"g cm"^(-3) xx10^(-12)cm^3=7.9xx10^(-12)` g
It is given that Avogadro number `(6.023xx10^(23))/(55) =8.65xx10^(10)` atoms.
The maximum possible dipole moment `m_(max)` is achieved for the (unrealistic) case when all the atomic moments are perfectly aligned.
Thus, `m_(max)= 8.65x10^(10)xx(9.27xx10^(-24))=8.0xx10^(-13)Am^2`
The consequent magnetisation is `M_(max)=(m_(max))/("Domain volume")`
`=8.0xx10^(-13)Am^2//10^(-18)m^3=8.0xx10^(5)Am^(-1)`
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Knowledge Check

  • A domain in a ferromagnetic substance is in the form of a cube of side length 1mum . If it contains 8 xx10^(10) atoms and each atomic dipole has a dipole moment of 9xx10^(-24) Am^2 , then the magnetization of the domain is

    A
    A) `7.2xx10^(5) Am^(-1)`
    B
    B)`7.2xx10^(3) Am^(-1)`
    C
    C) `7.2xx10^(9) Am^(-1)`
    D
    D) `7.2xx10^(12) Am^(-1)`

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