Calculate the radius and velocity of the electron in the `n^(th)` orbit in hydrogen atom from the following data `e=1.6xx10^(-19)C, m = 9.11 xx10^(-31) , h = 6.625xx10^(-34) JS, epsilon_(0) = 8.85xx10^(-12) " Fm "^(-1) and c = 3 xx10^(8) ms^(-1)`

Explanation

Given `e=1.6xx10^(-19)C, m = 9.11 xx10^(-31)kg, h = 6.625xx10^(-34) JS, epsilon_(0) = 8.85xx10^(-12) " Fm "^(-1) and c = 3 xx10^(8) ms^(-1)`
Radius `r_(n)=(epsilon_(0)n^(2)h^(2))/(pime^(2))`
`n^(2)xx((6.625xx10^(-34))^(2)(8.85xx10^(-12)))/(pixx(9.11xx10^(-31))(1.6xx10^(-19)))=5.3xx10^(-11)n^(2)m` ,
`v_(n)=(e^(2))/(2nhepsilon_(0))=((1.6xx10^(-19)))/(2n(6.625xx10^(-34))(8.85xx10^(-12)))=(2.18xx10^(6))/(n)ms^(-1)`