Calculate the most probable distance from the nucleus for an electron in the 2s state of...

Question

Question

Calculate the most probable distance from the nucleus for an electron in the 2s state of a helium ion (Het).

Answer 1

Answer #1

We find the radius at which the radial distribution function of the hydrogenic
orbital has a maximum value by solving dP/dr = 0.

P(r) = r2R(r)2

P2s = r2 ( 2- Zr/a0)2 *1/8 *(Z/a0)^3 *e−Zr/a0

dP/dr = 0 = r*( 2- Zr/a0)*1/8 *(Z/a0)^3 *(r^2/ao^2 - 6r/a0 + 4)*e−Zr/a0

on solving

r (m.p) =[(3 + 5^1/2)a0 /Z]

z=2 ;, a0 = 52.9 pm

r (m.p) ( for He+ in 2s )= 138 pm

Answer 2

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