The wavelength of the `K_(alpha)` line of X-ray of an element having atomic number Z=11 is `lambda`. For which atomic number will the wavelength of that line be `4lambda` ?

Explanation

Frequency, `f=c/(lambda) or, (f_1)/(f_2)=(lambda_2)/(lambda_1)=(4lambda)/(lambda)=4`
According to Moseley's law , `sqrt(f) porp (Z-1)`
`therefore (f_1)/(f_2)=((Z_1-1)/(Z_2-1))^2 or, ((Z_1-1)/(Z_2-1))^2= [here , Z_1=11]`
so, `(Z_2-1)^2=1/4xx(11-1)^2=1/4xx100=25`
`Z_2-1=5 or, Z_2=6`