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

A, B, D

Explanation

KEY CONCEPT :
we know that radius of nucleus is given by formula
`r = r_(0)A^(1//3) where r_(0) constt , and A = mass number `
`for the nucleus r_(1) = r_(0) 4^(1//3)`
for unknown nucleus `r_(2) = r_(0)4^(1//3)`
`:. (r_(2))/(r_(1)) = ((d)/(4))^(1//3) , (14)^(1//3)= ((A)/(4))^(1//3) rArr A = 56`
`:. `no of photon `= A - no of neucleus = 56 - 30 = 26`
`:. atomic number = 26 `
we know that ` v = Rc (Z - b)^(2)[(1)/(n_(1)^(2)) - (1)/(n_(2)^(2))]`
`here R = 1.1 xx 10^(7), c = 3 xx 10^(8) , Z = 26 `
` h = 1 (for k_(a)) , n_(1) = 1 , n_(2) = 2 `
`:. n = 1.1 xx 10^(7) xx 3 xx 10^(8) (26 - 1 )^(2) [(1)/(1) - (1)/(4)]`
`= 3.3 xx 10^(15) xx 25 xx 25 xx (3)/(4) = 1.546 xx 10^(16) Hz`