Determine the radius of the first orbit of the hydrogen atom. What would be the velocity and frequency of the electron in the first orbit ? Given : `h=6.62xx10^(-34) J s, m =9.1xx10^(-31) kg, e=1.6xx10^(-19) C, k = 9xx10^(9)m^(2)C.`

Explanation

Given `h=6.62xx10^(-34) J-s,`
`m=9.1xx10^(-31) kg`
`e=1.6xx10^(-19)C,`
`k=9xx10^(9)Nm^(2)C^(-2), n=1`
i) `r_(1)=(n^(2)h^(2))/(4pi^(2)" mke"^(2))`
`=((1)^(2)xx(6.62xx10^(-34))^(2))/(4xx(3.14)^(2)xx9.1xx10^(-31)xx9xx10^(9)(1.6xx10^(-19))^(2))`
`therefore r_(1)=0.529 overset(0)A cong 0.53 overset(0)A`
ii) `V=sqrt((KZ)/(mr))xxe`
`=sqrt((9xx10^(9)xx1)/(9.1xx10^(-31)xx0.53)xx1.6xx10^(-19)`
`therefore V=2.19xx10^(6) ms^(-1)`
iii) `v=(KZe^(2))/(nhr)`
`=(9xx10^(9)xx1xx(1.6xx10^(-19))^(2))/(1xx6.62xx10^(-34)xx0.529xx10^(-10))`
`therefore v=6.6xx10^(15)Hz.`