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Question

The time taken by the electron in one complete revolution in the nth Bohr's orbit of the hydrogen atom is:

A
Inversely proportional to n2
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B
Directly proportional to n3Z2
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C
Directly proportional to h2π
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D
Inversely proportional to nh
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Solution

The correct option is B Directly proportional to n3Z2

Time period of revolution 'T' of an electron in its orbit = 2πr/v
vn=2.18×106Zn ms1 where vn is the velocity of the electron
rn=0.529×n2Z A
where rn is the radius of nth orbit.
Z is the atomic number of the Hydrogen atom
On putting the values,
T = 2π×0.529n2Z2.18×106Zn
So, Time period T ∝ n3Z2


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