a.Calculate the velocity of an electron in the first Bohr's orbit of hydrogen atom (given `r = a_(0))`.
b. Find de Broglie's 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.

Explanation

(a)` mur = ( nh)/(2pi)`
` u = ( nh)/( 2 pimr) = ( 1 xx 6. 626 xx 10^(-34))/( 2 xx 3. 14 xx 9. 108 xx 10^(-31) xx 0, 529 xx 10^(-10))`
` 2. 19 xx 10 ^6 m//s`
(b) ` lambda = h/( mu) = ( 6.626 xx 10^(34))/(9. 108 xx 10^(-31) xx 2 . 19 xx 10 6)`
`= 3. 32 xx 10^(-10) m = 2 . 19 xx 10^6)`
` = 3.32 xx 10^(-10) m = 3.32Å `
( c) Orbital angular momentum of ` 2p` -orbital
` = sqrt ( l( 1 + 1)) = sqrt 2 [ h/( 2pi)] = h/( sqrt 2 pi) " "( :. l = 1 )`
` sqrt 2 xx h ( h = h 2 pi )`.