Question

An electron is revolving around the nucleus in a circular path of radius 'r'. with a uniform speed 'V'. give the direction of it's velocity and acceleration​

Answer 1

Answer :- Consider electron e is revolving around nucleus with speed v.

Period of revolution= velocity circumference

T= v 2πr ---- 1

Circulating current I= TTe ----- 2

= 2πr/vv

= 2πrev ---- 3

Definition :-

Magnitude of magnetic moment associated with the circular current is: MM =IA= 2πrev ×πr2---- 4

= 2evr ------- 5

Multiplying and dividing the right-hand side of equation (5) by the mass of

electron, me

then, M0

= 2mee(mmevr)---- 6

=2mee×L 0---- 7

Here L 0

=me

Definition :-

vr= angular momentum of the electron revolving around the nucleus.

The ratio of magnetic dipole moment with angular momentum of

revolving electron is called the gyromagnetic ratio.

Gyrometric ratio = L0M0

= 2mee

=8.8×1010 C/kg

Definition :-

Bohr magneton (symbol μB) is a physical constant and the natural unit for expressing the magnetic moment of an electron caused by either its orbital or spin angular momentum

The Bohr magneton is defined in SI units by

μB = 2me

ehμB

=9.274×10−24JT−1