Lesson test: Many-electron atoms

1.[2p]
Which term in the many-electron Hamiltonian prevents an exact solution?

The electron-electron repulsion $e^{2} / 4 π ε_{0} r_{i j}$

Correct

The kinetic energy of each electron

The answer is: The electron-electron repulsion $e^2/4\pi\varepsilon_0 r_{ij}$

The nuclear attraction $- Z e^{2} / 4 π ε_{0} r_{i}$

The answer is: The electron-electron repulsion $e^2/4\pi\varepsilon_0 r_{ij}$

The spin-orbit coupling

The answer is: The electron-electron repulsion $e^2/4\pi\varepsilon_0 r_{ij}$

2.[2p]
Using Slater's rules, what is the effective nuclear charge felt by a valence electron of fluorine ( $Z = 9$ )?

CorrectNot quite: 5.20

3.[2p]
In hydrogen, $2 s$ and $2 p$ have identical energy. In lithium, $2 s$ lies below $2 p$ . What breaks the degeneracy?

Penetration: the inner lobe of $2 s$ reaches inside the core where it is unshielded

Correct

The extra proton in the lithium nucleus

The answer is: Penetration: the inner lobe of $2s$ reaches inside the core where it is unshielded

The Pauli exclusion principle

The answer is: Penetration: the inner lobe of $2s$ reaches inside the core where it is unshielded

Relativistic correction to the electron mass

The answer is: Penetration: the inner lobe of $2s$ reaches inside the core where it is unshielded

4.[1p]
The $4 s$ orbital fills before $3 d$ , and $4 s$ electrons are also the first to be removed on ionisation.

True

Correct

False

The answer is: True

5.[2p]
What is the real basis of Hund's rule of maximum multiplicity?

Exchange energy: parallel spins require an antisymmetric spatial function, which keeps the electrons apart

Correct

Electrons in separate orbitals are further apart, so they repel less

The answer is: Exchange energy: parallel spins require an antisymmetric spatial function, which keeps the electrons apart

Half-filled subshells are inherently stable

The answer is: Exchange energy: parallel spins require an antisymmetric spatial function, which keeps the electrons apart

Parallel spins produce a magnetic attraction

The answer is: Exchange energy: parallel spins require an antisymmetric spatial function, which keeps the electrons apart

6.[2p]
Which ground-state configurations are correct?

Select all that apply

Cr is $[Ar] 3 d^{5} 4 s^{1}$

Correct

Cu is $[Ar] 3 d^{10} 4 s^{1}$

Correct

Fe²⁺ is $[Ar] 3 d^{4} 4 s^{2}$

The answer is: Cr is $[\text{Ar}]3d^5 4s^1$, Cu is $[\text{Ar}]3d^{10} 4s^1$, Pd is $[\text{Kr}]4d^{10}$

Pd is $[Kr] 4 d^{10}$

Correct

1.[2p] Which term in the many-electron Hamiltonian prevents an exact solution?

2.[2p] Using Slater's rules, what is the effective nuclear charge felt by a valence electron of fluorine (Z=9)?

3.[2p] In hydrogen, 2s and 2p have identical energy. In lithium, 2s lies below 2p. What breaks the degeneracy?

4.[1p] The 4s orbital fills before 3d, and 4s electrons are also the first to be removed on ionisation.

5.[2p] What is the real basis of Hund's rule of maximum multiplicity?

6.[2p] Which ground-state configurations are correct?

1.[2p]
Which term in the many-electron Hamiltonian prevents an exact solution?

2.[2p]
Using Slater's rules, what is the effective nuclear charge felt by a valence electron of fluorine ( $Z = 9$ )?

3.[2p]
In hydrogen, $2 s$ and $2 p$ have identical energy. In lithium, $2 s$ lies below $2 p$ . What breaks the degeneracy?

4.[1p]
The $4 s$ orbital fills before $3 d$ , and $4 s$ electrons are also the first to be removed on ionisation.

5.[2p]
What is the real basis of Hund's rule of maximum multiplicity?

6.[2p]
Which ground-state configurations are correct?