1.

Find the radius of the hydrogen atom in its ground state. Also calculate the velocity of the electron in n = 1 orbit. Given `h=6.63xx10^(-34)J s, m=9.1xx10^(-31) kg,` `e=1.6xx10^(-19)C, K=9xx10^(9)Nm^(2)C^(-2)`

Answer» `n=1, h=6.63xx10^(-34) J-s,`
`m=9.1xx10^(-31)kg`
`e=1.6xx10^(-19)C,`
`K=9xx10^(9) Nm^(2)C^(-2)`
i) `r=(n^(2)h^(2))/(4pi^(2)"mKe"^(2))`
`=((1)^(2)xx(6.63xx10^(-34))^(2))/(4xx(3.14)^(2)xx9.1xx10^(-31)xx9xx10^(9)xx(1.6xx10^(-9))^(2))`
`therefore r=0.5315 Å`
ii) `V=sqrt((KZ)/(mr))xxe`
`=sqrt((9xx10^(9)xx1)/(9.1xx10^(-31)xx0.53xx10^(-10)))xx1.6xx10^(-19)`
`therefore V=2.18xx10^(6) ms^(-1)`


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