Question

Calculate the value of ψ1s for the hydrogen atom, the He+ ion, and the Li2+ ion at r = 0, a₀, and 4a₀. Rationalize the trends in the values you obtain.

Answer 1

value of ψ1s for the hydrogen atom, the He+ ion, and the Li2+ ion would follow similar trends as He+ and Li2+ ions are Hydrogen like atoms.

For calculating the values of ψ1s we use the formula

ψ1s =e^-r/r0/ (r₀³)^1/2

takingr₀ = 5.29X 10^-11

For r = 0 we get,

e⁰/(3.14X (5.29X 10^-11)³)^1/2 = 0.465 X 10³²

For r = a0 or r0 we get,

e^-1/(3.14X (5.29X 10^-11)³)^1/2= 0.170 X 10³²

For r = 4a0 or 4 r0 we get,

e^-4/(3.14X (5.29X 10^-11)³)^1/2= 0.00850 X 10³²

therefore, we conclude that the values for the 1s orbital (ψ_1s) shows a decay for the wave function on moving away from the nucleus.