Explain quantitatively the order of magnitude diff ere nee between the diamagnetic susceptibility of `N_(2) (-5 xx 10^(-9) )` (at STP) and Cu `(-10^(-5) )`.

Explanation

Magnetic susceptibility is the property of the substance which shows how easily a substance can be magnetised.
Density of `N_(2)`,
`(rho)N_(2) =- (28 g) /( 22.4 L) = (28 g)/( 22,400 cm^(3) ) " "…(1)`
Density of copper,
`(rho)_(Cu) = (8g)/( cm^(3) )" "...(2)`
Taking the ratio of equation (1) and (2),
`therefore ((rho)N_2 )/( (rho ) Cu) = (((28)/( 22,400)))/( 8)`
`=0.0001562`
`=1.562 xx 10^(-4)`
`((rho) N)_(2) ) /( (rho)_(Cu) )= 1.6 xx 10^(-4)" "...(3)`
Magnetic susceptibility of given material,
`chi = ("Magnetisation (M)")/( " Magnetic intensity (H)")`
`= ("Magnetic dipole moment per volume")/( " H")`
`((("Magnetic dipole moment" m) /( "Volume V")))/(H)"`
`chi = (m) /( HV)" "...(4)`
but density `rho = ("mass" m.)/( "volume V")`
`therefore V= (m.)/( rho) " "...(5)`
`therefore chi = ((m)/( H_m) .) rho `
Taking terms of bracket as constant,
Thus `chi xx rho " "...(6)`
`therefore ((chi) N_2) /( (chi ) Cu) = ((rho) N_2) /((rho) (Cu) ) " "...(7)`
Putting the value of equation (3) in equation (7),
`((chi) N_2 )/( (chi) Cu ) = 1.6 xx 10^(-4) " "...(8)`