X rays are incident on a target metal atom having 30 neutrons. The ratio of the atomic radii of the target atom and `""_2He^4 " is " (14)^(1//3)`. What is the atomic number of the target atom ?

Options

A. 20
B. 26
C. 30
D. 40

Answer

B

Explanation

If `r_1 " and " r_2` are the atomic radii and `A_1 " and " A_2` are the mass number of the atom of the target metal and `"_2He^4` respectively then ,
`(r_1/r_2) = (A_1/A_2)^(1//3)`
`therefore (A_1/A_2) = (r_1/r_2)^3 = [ (14)^(1//3)]^3 = 14`
But `A_2 = 4 therefore (A_1)/(4) = 14 therefore A_1 = 56`
`therefore` In an atom of atomic number Z and atomic mass A, no. of electron = no. of protons = Z
`therefore` No. of neutrons = A - Z
`therefore` Z=A-No. of neutrons = 56 - 30 = 26
`therefore` Atomic number of target atom = 26