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NCERT Class XII Chapter
Atoms
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Question : 12
Total: 18
The gravitational attraction between electron and proton in a hydrogen atom is weaker than the coulomb attraction by a factor of about 10–40. An alternative way of looking at this fact is to estimate the radius of the first Bohr orbit of a hydrogen atom if the electron and proton were bound by gravitational attraction. You will find the answer interesting.
Solution:  
The radius of the first orbit in Bohr’s model is calculated by considering the electrostatic force between electrons and proton in nucleus.
r0 =
n2h2
4π2meke2
 where k =
1
4πε0
If we consider the atom bound by gravitational force
Gmpme
r2
 , then the term ke2 should be replaced by Gmpme. The radius of the first Bohr orbit ina gravitational bound hydrogen atom will be r′ =
n2h2
4π2Gmpme2
(1)2(6.6×10−34)2
4×9.87×.67×10−11×1.625×10−27×(9.1×10−31)2

r′ = 1.194 × 1029 m ≈ 1.2 × 1029 m.
This radius is much greater than the estimated size of the whole universe.
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