In accordance with the Bohr's model, find the quantum number that characterizes the earth's revolution around the sun in an orbit of radius `1.5xx10^(11)m` with orbital speed `3xx10^4m//s`. (Mass of earth=`6.0xx10^(24)kg`)

Explanation

Radius of the orbit of the Earth around the sun `r=1.5xx10^(11)m`
Orbital speed of the Earth `v=3xx10^(4)m//s`
Mass of the Earth `m=6.0xx10^(24)` kg
According to Bohr's model angular momentum is quatized and given as:
`mvr=(nh)/(2pi)`
Where,
h=Planck's constant `=6.62xx10^(-34)Js`
n=Quatum number
`:. n=(mvr2pi)/h`
`=(2pixx6xx10^(24)xx3xx10^(4)xx1.5xx10^(11))/(6.62xx10^(-34))`
`=25.61xx10^(73)=2.6xx10^(74)`
Hence, the quanta number that characterizes the Earth's revolution is `2.6xx10^(74)`