An electron is revolving in n = 3 orbit. What | vedclass

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(D) The magnetic field at the center of the orbit due to a revolving electron is given by $B = \frac{\mu_0 i}{2r}$.Here,the current $i = \frac{e}{T} =

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$0.05$

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(D) The magnetic field at the center of the orbit due to a revolving electron is given by $B = \frac{\mu_0 i}{2r}$.Here,the current $i = \frac{e}{T} = \frac{ev}{2\pi r}$.Substituting $i$,we get $B = \frac{\mu_0 ev}{4\pi r^2}$.For the $n$-th orbit of a hydrogen atom,the velocity is $v_n = \frac{v_1}{n} = \frac{2.18 	imes 10^6}{3} \approx 7.27 	imes 10^5 \ m/s$.The radius is $r_n = r_1 n^2 = 0.529 	imes 10^{-10} 	imes 3^2 = 4.761 	imes 10^{-10} \ m$.Substituting these values into the formula:$B = \frac{(10^{-7}) 	imes (1.6 	imes 10^{-19}) 	imes (7.27 	imes 10^5)}{(4.761 	imes 10^{-10})^2}$.$B = \frac{1.1632 	imes 10^{-20}}{22.667 	imes 10^{-20}} \approx 0.0513 \ T$.Rounding to the nearest option,the value is $0.05 \ T$.

An electron is revolving in $n = 3$ orbit. What will be the magnetic field at the centre of the hydrogen atom? (in $T$)

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