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Q.

According to Bohr’s theory, the time-averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the $n^{th}$ orbit is proportional to $n^{- x}$ the value of ‘ $x$ ’ is(n = principal quantum number)

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answer is 5.

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Detailed Solution

Magnetic field at the center $B_{n} = μ_{0} l / 2 r_{n}$

For a hydrogen atom, the radius of $n^{t h}$ orbit is given by

$r_{n} \propto n^{2}$

$l = e / T = e / (2 π r_{n} / v_{n}) = e v_{n} / 2 π r_{n}$

$A l s o v_{n} \propto n^{- 1} ∴ l \propto n^{- 3}$

$H e n c e, B_{n} \propto n^{- 5}$

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According to Bohr’s theory, the time-averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the nth orbit is proportional to n−x the value of ‘x’ is(n = principal quantum number)