CBSE Class 12 Physics 2015 Delhi Set 1 Paper

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Question : 7
Total: 26
Show that the radius of the orbit in hydrogen atom varies as n2, where n is the principal quantum number of the atom.
Solution:  
Showing that the radius of orbit varies as n2
mv2
r
=
1
4πε0
e2
r2

or mv2r=
1
4πε0
e2
.......(i)
mvr=
nh
2π

m2v2r2=
n2h2
4π2
.......(ii)
Divide (ii) by (i)
mr=
n2h2
4π2
×
4πε0
e2

r=
n2h2
4π2me2
4πε0

rn2
(Give full credit to any other correct alternative method)
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