7.3.3 Atomic Orbital Energy

Question 1

Atomic Orbital Energy

Answer 1

• When an electron is infinitely separated from a nucleus, the energy is defined to be zero.
• For a hydrogen atom, the principal quantum number indicates the energy level of the electron.

Question 2

note

Answer 2

• When an electron is infinitely separated from a nucleus, the energy is defined to be zero.
• The 1s orbital is the lowest energy state of an electron.
• As an electron moves from a lower energy level to a higher energy level, its energy becomes closer to zero. Energy is required to move an electron to a higher energy level.
• As the principal quantum number increases, the average distance of an electron from a nucleus increases. Therefore, the energy gets closer to zero.
• The energy of an electron in hydrogen (E n ) is equal to
  negative one multiplied by the Rydberg constant (R)
  multiplied by the nuclear charge (Z) squared, divided by
  the principal quantum number (n) squared. For hydrogen, the only variable is n. Therefore, for the hydrogen atom, the principal quantum number (n) indicates the energy level of the electron.
• The solutions to the Schrödinger equation accurately predict the behavior of any atom that contains only one electron (any hydrogen-like atom, such as He + , Li 2+ , or Be 3+ ). However, since these solutions do not take into account the interactions between electrons, they do not accurately predict the behavior of atoms with more than one electron.

Question 3

How does the nuclear charge relate to the size of the 1s orbital and the energy of the orbital?

Answer 3

The orbital size decreases and the energy of the orbital becomes more negative as the nuclear charge increases.

Question 4

What is the energy of an electron in the 2s orbital of a hydrogen atom?

Answer 4

−5.45 × 10^−19 J

Question 5

How much energy is required to move the electron of the hydrogen atom from the 1s to the 2s orbital?

Answer 5

1.64 × 10^−18 J

Question 6

Electrons in the 2s and 2p orbitals have _______________ quantum numbers n and electrons in the 2s and 3s orbitals have _____________ quantum numbers n.

Answer 6

the same; different

Question 7

For which of the orbitals below is the electron closest to the nucleus?

Answer 7

2s

Question 8

Determine the frequency of light required to move the electron of the Be3+ ion from the n = 1 to the n = 4 orbital. The atomic number of beryllium is 4.

Answer 8

4.94 × 10^16 s−1

Question 9

Determine the energy of an electron that would be assigned for n = 4 for the Li 2+ ion.

Answer 9

−1.23 × 10^−18 J

Question 10

What frequency of light would cause the electron of a Li2+ ion to be ejected from the 1s orbital? The energy needed to remove this electron is 1.96 × 10^−17 J.

Answer 10

2.96 × 10^16 s−1

Question 11

Determine the energy required to remove the electron from the 1s orbital of a Helium ion (He+ ).

Answer 11

8.72 × 10^−18 J

Question 12

When does an electron have zero energy?

Answer 12

When it has been removed from the atom.