A `10kg` satellite circles earth once every `2hr` in an orbit having a radius of `8000km`. 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

Given,
Mass of satellite, m=10 kg
Time period of revolution, T=2hours=2 x 60 x 60
=7200 s
Radius of orbit, r=8,000 km
`=8,000 xx 10^3` m
`=8xx10^6` m
According to the Bohr.s quantisation condition the angular momentum is given by
`L=mvr=(nh)/(2pi)`
where v=velocity of satellite
n=quantum number of satellite
`rArr (mxx2pir)/T xxr =(nh)/(2pi) " " [because v=(2pir)/T]`
`rArr n=(4pi^3r^2m)/(Th)`
`=(4xx(3.14)^2xx(8xx10^6)^2xx10)/(7200xx6.63xx10^(-34))`
`=5.28xx10^45=5.3xx10^45`