The magnetic susceptibility of a paramagnetic substance at ` - 173^(@)` C is ` 1 . 5 xx 10^(-2)` . To have the susceptibility `0 . 5 xx 10^(-2)` , the change in temperature in `.^(@)C` is

Options

A. 100
B. 180
C. 200
D. 220

Answer

C

Explanation

Given, magnetic susceptibility of a paramagnetic substance, `X_(m_(1)) = 1.5 xx 10^(-2)`
`T_(1) = - 173^(@) C`
`= (-173 +273) = 100K`
`X_(m_(2)) =0 . 5 xx 10^(-2)`
According to the Curie.s law.
`X_(m) prop (1)/(T) or (X_(m_(1)))/(X_(m_(2)))= (T_(2))/(T_(1))`
`rArr T_(2) = T_(1) ((X_(m_(1)))/(X_(M_(2))))`
`rArr T_(2) = 100 ((1.5 xx 10^(-2))/(0 . 5 xx 10^(-2)))= 300 K`
`T_(2) = (300- 273)`
`T_(2) = 27^(@) C`
Hence, change in temperature, `Delta T = T_(2) - T_(1)`