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 )/(lambda_(2)))a=(Z_(2)-b)`....(ii)
From (i) and (ii) `sqrt(c )((1)/(sqrt(lambda_(1)))-(1)/(sqrt(lambda_(1))))=a(Z_(1)-Z_(2)` ,
or, `a=(sqrt(c ))/((Z_(1)-Z_(2)))((1)/(sqrt(lambda_(1)))-(1)/(sqrt(lambda_(2))))`
`=((3xx10^(8)m//s)^(1//2))/(42-27)[(1)/((71xx10^(-12)m)^(1//2))-(1)/((178.5xx10^(-12)m)^(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`