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In the hydrogen atom, an electron revolv...

In the hydrogen atom, an electron revolve around a proton in a circular orbit of radiu 0.53 A. The radial acceleration and the angular velocity of the electron are......and…………. `(m_(e) = 9.1 xx 10^(-31) kg, e = 1.6 xx 10^(-19)`C)

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Suppose, charge on a proton and an electron is e The electric force between them at distance d will be:
`F = (ke^(2))/r^(2)`
`=(9 xx 10^(9) xx (1.6 xx 10^(-19))^(2))/(0.53 xx 10^(-10))^(2)`
`= 82.02 xx 10^(-9)`
`therefore F = 8.2 xx 10^(-8)` N
The centripetal acceleration `=("Centripetal force")/("mass")`
`therefore a_( c) = F/m`
[Mass of electron, `m_(e) = 9.1 xx 10^(-31) kg`]
`=(8.1 xx 10^(-8))/(9.1 xx 10^(-31))`
`therefore a_( c) = 0.9 xx 10^(23) m//s^(2)`
Centripetal force `=(mv^(2))/r = (mr^(2)omega^(2))/r [therefore v= romega]`
`therefore F = mromega^(2)`
`therefore omega = [F/(mr)]^(1/2)`
`=[17 xx 10^(32)]^(1//2)`
`therefore omega = 4.1 xx 10^(16)` rad/s
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