Question

Find the velocity (in `m s^(-1)`) of electron in first Bohr orbit of radius `a_(0)`. Also find the de Broglie wavelength (in m). Find the orbital angular momentum of 2p orbital of hydrogen atom in units of `h//2pi`.

Answer 1

For H and H-like particles, velocity in the nth orbit
`v_(n) = 2.188 xx 10^(6) xx (Z)/(n) ms^(-1)`
For H-atom, Z = 1 and for 1st orbit n = 1
`:. v = 2.188 xx 10^(6) ms^(-1)`
de Broglie wavelength, `lamda = (h)/(mv) = (6.626 xx 10^(-34) kg m^(2) s^(-1))/(9.1 xx 10^(-31) kg xx 2.188 xx 10^(6) ms^(-1)) = 3.33 xx 10^(-10) m`
Orbital angular momentum `= sqrt(l(l + 1)) (h)/(2pi)`
For 2p orbital, `l = 1`
`:.` Orbital angular momentum `= sqrt(1(l + 1)) (h)/(2pi) = sqrt2 (h)/(2pi)`