X-ray are incident on a target metal atom having 30 neutrons. The ratio of atomic radius of the target atom and He nucleus is `(14)^(1//3)`. (a) Find the mass number of target atom.
(b) Find the frequency of `K_alpha` line emitted by this metal.
Hint : Radius of a nucleus (r) has the following relation with mass number (A). `r prop A^(1//3)`
`(R = 1.1xx10^8 m^(-1) , C =3xx10^8 m//s)`

Answer

(i) `26` (ii) `1.55 xx 10^(18) Hz`

Explanation

(i) from the relation `r prop A^(1//3)`
We have `r_(1)/r_(2)=(A_(1)/A_(2))^(1//3) implies (A_(2)/4)^(1//3)=(14)^(1//3)`
`:. A_(2)=56`
(ii) `Z_(2)-A_(2)-` no. of neutrons `=56-30=26`
`:. F_(ka)=Rc (Z-1)^(2)(1/1^(1)-1/2^(2))=(3Rc)/4 (Z-1)^(2)`
Subtituting the given values of R, c and Z.
We get `f_(ka)=1.55xx10^(18) Hz`