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A domain in ferromagnetic iron is in the...

A domain in ferromagnetic iron is in the form of a cube of side length `10^-4m`. Estimate the number of iron atoms in the domain and the maximum possible dipole moment and magnetisation of the domain. The molecular mass of iron is `55g//"mole"`, and its density is `7*9g//cm^3`. Assume that each iron atom has a dipole moment of `9*27xx10^(-24)Am^2`.

A

` 8xx10^(5)A-m^(-2)`

B

`4xx10^(5) A-m^(-1)`

C

` 8 xx 10^(-13)A-m^(2)`

D

`8 xx 10^(13) A-m^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
The volume of the cubic domain is ` V=(10^(-6)m)^(3)=10^(-18)m^(3)=10^(-12)cm^(3)`
Its mass is volume ` xx ` density `=7.9 g cm^(-3) xx 10^(-12)cm^(3)=7.9 xx 10^(-12)g `
It is given that an Avogadro's number `(6.023 xx 10^(23))` of iron atom have a mass of 55 g. Hence , the number of atoms in the domain is
` N=(7.9 xx 10^(-12) xx 6.023 xx 10^(23))/(55)`
`N=8.65 xx 10^(10)` atoms
The maximum possible dipole moment `M_("max")` is achieved for the case when all the atomic moments are perfectly aligned . Thus , `M_("max")=(8.65 xx 10^(10)) xx (9.27 xx 10^(-24))=8.0xx10^(-13)A-m^(2)`
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