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Question : 4
Total: 4
(a) Use Bohr's postulate to prove that the radius of n th n 2
(b) How will the energy of a hydrogen atom change ifn ∞
(b) How will the energy of a hydrogen atom change if
Solution:
The necessary centripetal force for the rotation of electron is supplied by the electrostatic force between the electron and nucleus.
= (
) (
) [ putting Z = 1 ]
Or,m v 2 =
. . . . . . . . . . ( i )
From Bohr's theory,
m v r =
∴ v =
Putting in equation (i)
m (
) 2 =
Or,r =
In general,
r n =
∴ r n ∝ n 2
(b)E n ∝ −
Energy is minimum atn = 1
Asn
Or,
From Bohr's theory,
Putting in equation (i)
Or,
In general,
(b)
Energy is minimum at
As
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