Question

In the Bohr model of the hydrogen atom, the electron circuulates around the nucleus in a path of radius `5xx10^-11m` at a frequency of `6.8xx10^15Hz`.
a. What value of magnetic field is set up at the centre of the orbit?
b. What is the equivalent magnetic dipole moment?

Answer 1

a. An electron moving around the nucleus is equivalent to a current,
Magnetic field at the centre,
`B=(mu_0i)/(2R)=(mu_0qf)/(2R)`
Substituting the values, we have
`B=((4pixx10^-7)(1.6xx10^-19)(6.8xx10^15))/(2xx5.1xx10^-11)`
`=13.4T`
b. The current carrying circular loop is equaivalent to a magnetic dipole with magnetic dipole moment,
`M=NiA=(NqfpiR^2)`
Substituting the values, we have
`M=(1)(1.6xx10^19)(6.8xx10^15)(3.14)(5.1xx10^-11)^2`
`=8.9xx10^-24A-m^2`