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Prove the the velocity of electron revol...

Prove the the velocity of electron revolving in the 1st orbit of H-atom is nearly `10^(-2)` times that of light.

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According to Bohr's theory, `mvr=(nh)/(2pi)` . . . [1]
Radius of 'n' the orbit, `r=(n^(2)h^(2))/(4pi^(2)mZe^(2))` . . . [2]
From equations [1] and [2], we have,
`(nh)/(2pimv)=(n^(2)h^(2))/(4pi^(2)mZe^(2))`
or, `(1)/(v)=(nh)/(2piZe^(2)) or, v=(2piZe^(2))/(nh)`
For hydrogen atom, Z=1, Hence, `v=(2pie^(2))/(nh)` . . [3]
For the first orbit, n=1, `e=4.8xx10^(-10)` esu,
`h=6.627xx10^(-27_erg*s`
`therefore`The velocity of moving electron in the first orbit
`v=(2xx3.14xx(4.8xx10^(-10))^(2))/(1xx6.627xx10^(-27))`
`=2.183xx10^(8)=(2.183xx10^(10))xx10^(-2)cm*s^(-1)`
Again, the velocity of light`=3xx10^(10)cm*s^(-1)`
Hence, the velocity of electron revolving in the first orbit of H-atom is almost `10^(-2)` times of the velocity of light.
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