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Question

According to Bohr's model of hydrogen atom, relation between principal quantum number n and radius of stable orbit is

A
r1n
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B
rn
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C
r1n2
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D
rn2
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Solution

The correct option is D rn2
Let an electron (mass m), is revolving around nucleus of a hydrogen atom in an orbit of radius r with velocity v. Electron gets centripetal force to revolve, from the electrostatic attraction force between electron and nucleus,
mv2r=e×e4πε0r2 (for H- atom, Z=1 hence charge on nucleus is =e)
mv2=e24πε0r ...................eq1

According to Bohr's model, angular momentum of electron :
mvr=nh2π ..................eq2

Now, squaring eq2 and dividing by eq1, we get
mv2r2mv2=n2h24πε0r4π2e2

r=n2h2ε0πme2

which gives rn2

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