JEE Advance - Chemistry (2005 - No. 3)
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 $$h/2 \pi$$.
v = 2.18 x 106 ms-1, λ = 3.34 x 10-10 m, L = $$\sqrt{2} \frac{h}{2\pi}$$
v = 2.18 x 10-6 ms-1, λ = 3.34 x 10-10 m, L = $$\sqrt{2} \frac{h}{2\pi}$$
v = 2.18 x 106 ms-1, λ = 3.34 x 1010 m, L = $$\sqrt{2} \frac{h}{2\pi}$$
v = 2.18 x 106 ms-1, λ = 3.34 x 10-10 m, L = 2$$\frac{h}{2\pi}$$
v = 2.18 x 106 ms-1, λ = 3.34 x 10-10 m, L = $$\frac{h}{2\pi}$$
Explanation
For hydrogen atom;
z = 1, n = 1
or, v = 2.18 $$\times$$ 106 ms$$-$$1
de-Broglie's wavelength, $$\lambda = {h \over {mv}}$$
$$ = {{6.626 \times {{10}^{ - 34}}kg\,{m^2}{s^{ - 1}}} \over {9.11 \times {{10}^{ - 31}}kg \times 2.18 \times {{10}^6}\,m{s^{ - 1}}}}$$
$$ = 3.34 \times {10^{ - 10}}\,m$$
Orbital angular momentum
$$ = \sqrt {l(l + 1)} .\,{h \over {2\pi }}$$
For 2p-orbital, l = 1
$$\therefore$$ Orbital angular momentum $$ = \sqrt 2 \,.\,h/2\pi $$.
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