The total Is wave function for any one electron atom is given by, psi_1s = 1/Squ

Question

The total Is wave function for any one electron atom is given by, psi_1s = 1/Squareroot pi (z/a_0)^3/2 e^-zr/a_0 where Z is the nuclear charge. Determine the position of the maximum in the corresponding radial distribution function. Show that the wave function is normalized. Then determine the average distance of the 1s electron from the nucleus, in terms of the Bohr radius a_0 and the nuclear charge Z, for any one electron atom or ion. You will need to use the following standard integral for the last two parts, The energies levels for a one electron atom or ion are given by, Calculate the ionization energies for the hydrogen atom and the He+ ion. Do the results make sense? Why?

Explanation / Answer

For hydrogen Z=1, n=1

= - 2. 18 X 10-18 J

For He+ Z= 2 , n=1

= - 2. 18 X 10-18 J * 22/12

= - 4. 36 X 10-18 J

Due to presence of more nucleus charge on He for removal of single electron we need more energy than hydrogen

Because hydrogen have one proton in nucleus helium have 2 protons

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