Question

Highly energetic electron are bombarded in a target of an element containing `30` neutrons Tne ratio of nucleus to that of Helium nucleus is `(14)^(1//3)` . Find (a) atomic number of the nucleus (b) the frequency of `k_(a)` line of the X- rays producted `(R = 1.1 xx 10^(7) m^(-1) and c = 3 xx 10^(8)m//s)`

Answer 1

(a) From the relation `r prop A^(1//3)` ,
We have `(r_2)/(r_1) = ((A_2)/(A-1))^(1//3)`
or ` ((A_2)/(4))^(1//3) ` (14(^(1//3)
:. `A_2 =56`
(b) `Z_2 = A_2 ` number of neutrons
`=56 - 30 =26`
`:. F = Rc(Z-1)^2 ((1)/(1^2) - (1)/(2^2)) = (3Rc)/(4) (Z-1)^2`
Substituting the given values of R, c and Z, we get
` f= 1.55xx10^18 Hz`