Find the constants a and b in Moseley's equation `sqrt v=a(Z- b)` from the following data.

Explanation

Moseley's equation is
`sqrt v = a(Z-b)`.
Thus, `sqrt(c/lambda_1)) = a(Z_1-b)` …(i)
and `sqrt(c/(lamda_2)) = a(Z_2 - b)` …(ii)
From (i) and (ii),
`sqrt c(1/(sqrt (lambda_1))-1/(sqrt (lambda_2))) = a(Z_1-Z_2)`
or, `a = (sqrtc)/((Z_1-Z_2))(1/sqrt (lamda_1)-1/sqrt(lambda_2))`
`(3x10^(8)ms^(-1))^(1/2)/(42-27)[(1)/((71xx10^(-12) m)^(1/2))-(1)/((178*5xx10^(-12) m)^(1/2))]`
` 5*0 xx 10 ^ (7) (Hz) ^(1/2)`.
Dividing (i) by (ii),
`sqrt((lambda_2)/(lambda_1))= (Z_1-b)/(Z_2-b)`
or, `sqrt(178.5/71) = (42-b)/(27-b)`
or, `b= 1.37`.