Find the velocity (ms^-1) of electron in first Bohr's orbit of radius a₀. Also find the de Broglie's wavelength (in m). Find the orbital angular momentum of 2p orbital of hydrogen atom in units of $$h/2 \pi$$.

(a) The Schrodinger wave equation for hydrogen atom is

$$$\psi = {1 \over {4\sqrt {2\pi } }}{\left( {{1 \over {{a_0}}}} \right)^{3/2}}\left( {2 - {{{r_0}} \over {{a_0}}}} \right){e^{ - {r_0}/{a_0}}}$$$
Where a₀ is Bohr's radius. If the radial node in 2s be at r₀, then find r₀ in terms of a₀.

(b) A baseball having mass 100 g moves with velocity 100 m/s. Determine the value of wavelength of baseball.

A ball of mass 100 g is moving with 100 ms^-1. Find it's wavelength.

Wavelength of high energy transition of H-atoms is 91.2 nm. Calculate the corresponding wavelength of He atoms.