An electron in a circular orbit of radius 0.0 | vedclass

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(D) Given:Radius $r = 0.05 \ nm = 0.05 	imes 10^{-9} \ m$Frequency $f = 10^{16} \ Hz$ (revolutions per second)Charge of electron $e = 1.6 	imes 10^{

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$1.26 	imes 10^{-23}$

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(D) Given:Radius $r = 0.05 \ nm = 0.05 	imes 10^{-9} \ m$Frequency $f = 10^{16} \ Hz$ (revolutions per second)Charge of electron $e = 1.6 	imes 10^{-19} \ C$The magnetic moment $M$ of a current loop is given by $M = I 	imes A$, where $I$ is the current and $A$ is the area of the loop.The current $I$ due to the revolving electron is $I = e 	imes f$.The area of the circular orbit is $A = \pi r^{2}$.Substituting these into the formula for magnetic moment:$M = (e 	imes f) 	imes (\pi r^{2})$$M = (1.6 	imes 10^{-19} \ C) 	imes (10^{16} \ s^{-1}) 	imes (3.14) 	imes (0.05 	imes 10^{-9} \ m)^{2}$$M = 1.6 	imes 10^{-19} 	imes 10^{16} 	imes 3.14 	imes 0.0025 	imes 10^{-18}$$M = 1.6 	imes 3.14 	imes 0.0025 	imes 10^{-21} \ m^{2} \cdot C/s$$M = 0.01256 	imes 10^{-21} \ A \ m^{2}$$M = 1.26 	imes 10^{-23} \ A \ m^{2}$

An electron in a circular orbit of radius $0.05 \ nm$ performs $10^{16}$ revolutions per second. The magnetic moment due to this rotation of the electron is (in $A \ m^{2}$):

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