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.

Options

A. `5.3xx10^40`
B. `5.3xx10^45`
C. `7.8xx10^48`
D. `7.8xx10^50`

Answer

B

Explanation

Here, `m=10kg, r_n=8xx10^6)m T=2xx60xx60=7200s`
Velocity of `n^th` orbit, `v_n=(2pir_n)/(T)` and from `mv_nr_n=(nh)/(2pi)`
`n=(2pi)/(h)xxmxx(2pir_n)/(T)xxr_n`
`=(2pir_n)^2xx(m)/(Txxh)=((2pixx8xx10^6)^2xx10)/(7200xx6.64xx10^(-34)`
`=5.3xx10^(45)`.