Question

show that the radius of the orbit in hydrogen atom varies as n2 where n is the principle quantum number of the atom

Answer 1

Answer:

Answer

According to Bohr's second postulate, mvr=2πnh

where m be the mass of an electron, v be the velocity and r be the radius of orbit in which the electron revolves around the nucleus.

So, v=2πmrnh

Here, the centripetal force is provided by the electrostatic force of attraction between electron and nucleus. 

Thus, rmv2=r2k(Ze)(e)

⇒r=mv2kZe2

Substituting the value of v:

r=4π2mkZe2n2h2

Thus, r∝n2

Explanation:

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