The key feature of Bohr'[s spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton we will extend this to a general rotational motion to find quntized rotantized rotational energy of a diatomic molecule assuming it to be right . The rate to energy applied is Bohr's quantization condition
In a `CO` molecule, the distance between `C (mass = 12 a. m. u ) and O (mass = 16 a.m.u)` where 1 a.m.u = (5)/(3) xx 10^(-27) kg , `is close to

Options

A. `2.4 xx 10^(-10) m `
B. `1.9 xx 10^(-10) m `
C. `1.3 xx 10^(-10) m `
D. `4.4 xx 10^(-11) m `

Answer

C

Explanation

Contre of mass divides the distance between the point masses in inverse ratio their masses
:. R_(1) = (m_(2) d)/(m_(1) + m_(2)) and r_(2) = (m_(2) d)/(m_(1) + m_(2)) `
Also the moment of the system is
1 m_(1)r_(1)^(2) + m_(2) r_(2)^(2)`
`rArr 1.87 xx 10^(-46) = 12 xx (5)/(3) xx 10^(-27) [(16 xx (5)/(3) xx 10^(-27) xx d)/(28 xx (5)/(3) xx 10^(-27))]^(2)`
+16 xx (5)/(3) xx 10^(-2) [(12 xx (5)/(3) xx 10^(-27) xx d)/(28 xx (5)/(3) xx 10^(-27))]^(2)`
`rArr d= 1.3 xx 10^(-10) m `