Calculate the velocity of an electron in the first Borh's orbit of hydrogen atom (given `r = a_(0))`
b. Find de Broglie wavelength of the electron in the first Bohr's orbit
c. Find the orbital angular momentum of `2p` orbital in terms of `h//2pi` units

Answer

A, B, C

Explanation

For a Bohr's norbit,
`v= 2.188 xx 10^(6) xx (Z)/(n) cm s^(-1)`
For the first of hydrogen atom
`v= 2.188 xx 10^(6) xx (1)/(1) cm s^(-1)= 2.188 xx 10^(6) xx (Z)/(n) cm s^(-1)`
`mvr = n(h)/(2pi) `(Bohr's model)
`v= n(h)/(2pi)(1)/(mr)`
Given `r = a_(0) = 0.529 xx 10^(-10)m`
`v= 1 xx (6.626 xx 10^(-34))/(2 xx 3.14) xx (1)/(9.1 xx 10^(-31) xx 0.529 xx 10^(-10))`
`= 2.188 xx 10^(6) ms^(-1)`
b.`lambda = (h)/(mv) ("de Broglie's equation") `
`= (6.626 xx 10^(-34))/(9.1 xx 10^(-31) xx 2.188 xx 10^(6)) `
`= 3.337 xx 10^(-10) m `
c. The orbital angular momentum is `(h)/(2pi) sqrt(l(l + 1))` THe orbital angular momentum for an electron in `2p ` orbital `(l = 1) is (h)/(2pi) sqrt(l(l + 1)) = (h)/(2pi) sqrt(2)`