Question

Answer d

a. (4 points) Write the Hamiltonian for the neutral Li atom, explicitly including each kinetic and potential energy term. b. (4 points) For a one-electron atom, the 2s and 2p orbitals are degenerate. Why does one electron in Li occupy the 2s orbital instead of 2p? How does that relate to the expectation values for the radii of 2s and 2p you computed earlier on this homework? c. (4 points) Li has an ionization energy of 5.39 eV. Based on this value, approximate Zeff for the 2s electron in Li. d. (5 points) Based on your answer to the previous question, what is the expectation value for the radius of the 2s electron in Li? Explain why is the size of Li is different from the size of a hydrogen atom with its electron in the 2s orbital.

Answer 1

Ans d :

Radius of Lithium is

1.86.4

Volume of Li

تهران

= 1.33×3.14×1.86×1.86×1.86

= 26.87

Electronic configuration of Li =

15-25

Radius of Hydrogen is 0.53 A0

Volume of Hydrogen

تهران

= 1.33×3.14×0.53×0.53×0.53

= 0.62

Electronic configuration of H= 1s1

Hence volume of Lithium for 2s electron is more than Volume of Hydrogen in 2s . And moreover in hydrogen there is no 2s electron.

Thank you.