Question

42. Verify that the average value of 1/r in a hydrogen-like 3d orbital is given by 9a

Answer 1

For a hydrogen like atom, the radius r is given by

-----(1)

4π h2 γ = 4π2ze3μ

Where $\varepsilon$₀ is the permittivity of free space,

n is the principal quantum number of the shell

h is the planck's constant

z is the atomic number

e is electronic charge

$\mu$ is the reduced mass

For hydrogen, the bohr radius is given by

----------(2)

4π ε, h2 αο - 4π2e2μ

Dividing (2) by (1) we get,

---------(3)

For 3d shell, n = 3, therefore

1 z 7900