In the hydrogen atom, the light-weight electron is attracted to the much heavier

Question

In the hydrogen atom, the light-weight electron is attracted to the much heavier nucleus by the Coulomb force. This is analogous to the gravitational attraction between a light-weight planet and the sun; both Coulomb and grav- itational forces grow weaker with distance as 1/r2, and in both it is a good approximation to treat the heavier of the two objects as fixed in space, while the lighter of the two orbits around it. In one of the first attempts to include quantum mechanical corrections for the orbiting electron in the hydrogen atom, Niels Bohr suggested (1913)

Explanation / Answer

angular momentum,

L=m*v*r=n*(h/2pi) --(1)

a)

current i=e/t

i=e/(2pi*r/v)

i=e*v/(2pi*r)

i=e*V/(2pi*r)

b)

magnetic moment(M) =i*A

direction is out of the page

c)

magnetic moment, M=i*A

=e*V/(2pi*r)*(pi*r^2)

=e*v*r/2

=(e/2)*(n*h/2pi*m) ( from equation no (1))

=n*(e*h/4pi*m)

for n=1,

M=e*h/(4pi*m) ----> is called Bohr magnet

and

M=(1.6*10^-19*6.63*10^-34)/(4pi*9.1*10^-31)

M=9.27*10^-24 A*m^2 or Joule*T

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