A 10 kg satellite circles earth once every 2 h in an orbit having a radius of `8000 km. Assuming that Bohr's angular momentum postulate applies to satellites just as it does to an electron in the hydrogen atom, find the quantum number of the orbit of the satellite.

Explanation

From equation, we have
`mv_(n)r_(n)=nh//2pi`
Here `m = 10 kg and r_(n)=8xx10^(6)m.` We have the time period T of the circling satellite as 2h. That is T=7200 s.
Thus the velocity `v_(n)=2pi r_(n)T`
The quantum number of the orbit of satellite
`n=(2pi r_(n))^(2)xxm (Txx h)`
Substituting the values,
`n=(2pi xx8xx10^(6)m)^(2)xx10//(7200 s xx 6.64xx10^(-34)J s)`
`=5.3 xx 10^(45)`
Note that the quantum number for the satellite motion is externely large ! In fact for such large quantum number the results of quantisation conditions tend to those of classical physics.