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.

Find the velocity (in m s^(-1)) of electron in first Bohr orbit of rad

1.	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» Solution :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)`