Question

1. The “particle in the box” problem uses simplifications that allow us to treat Schrödinger’s equation without the use of computers. a. List these assumptions and show how they simplify the applications of the Hamiltonian operator. b. Why aren’t d subshells found in the second shell? c. Why are there seven f atomic orbitals in an f subshell? d. What are possible combinations of the four quantum numbers for an electron in 5f atomic orbitals?

Answer 1

a:Assumptions for the derivation of Schrodinger equation :

T+U=E

Where T is kinetic energy

U is potential energy and

E is total energy

Hamiltonian operator :

The sum of kinetic energies + potential energies for all particles in the system gives the total energy of the system. It is denoted by H.

b. The total number of subshells are s,p,d and f. In first shell only one subshell is found that is s subshell. Similarly, in second shell (n=2),only two subshells are possible. They are s and p sub shells. So, d subshell is not possible in second shell.

c. The first set of f orbitals is the 4f subshell. There are 7 possible magnetic quantum numbers,so there are 7 f orbitals.

d. The possible combinations of all four quantum numbers of 5f orbitals are

n=5,

l= n-1=4,

ml=-l+3=-1,

ms= +1/2 or -1/2.