[기출문제] KAIST 일반화학 2025-1 중간 기출문제 (정답 포함)

1. (7 points)
In the hydrogen atom, the electronic transition from the 2p state to the 1s state involves an emission
of a photon with energy 16.2 10-19 J. In an iron atom, the same transition (from 2p to 1s) results in
an emission of an X-ray of wavelength 0.193 nm.
(1) Calculate the energy difference between these two states in iron (3 pts).
(2) Explain the difference in the 2p-1s energy level spacing in these two atoms (4 pts).

2. (8 points)
You have learned about the 2p and 3d orbitals both in terms of their energy levels and pictures of
their overall shape (features including lobes, nodes, etc).
(1) State the number of nodes in the 3pz and 4dz2 orbitals (2 pts).
(2) Compare the relative energies of the 3s, 3p, and 3d orbitals in the following cases: (6 pts)
(a) a hydrogen atom, and
(b) a multi-electron atom with an effective nuclear charge (Zeff).
Briefly explain the differences.

3. (10 points)
(a) The ionization energies for the 1s electron for the second-row elements are as follows:
(Reminder: the 1s is a core orbital not outer orbital; Notes: IE of the first electron only; the atoms are
neutral, not ion their ionic form; measurements are in gas phase):

Now suppose that a certain substance is bombarded by X-rays of wavelength 0.989 nm. If
photoelectrons with kinetic energies of 94,000 kJ/mol and 69,900 kJ/mol are ejected from the material,
which of the elements listed above must be present in the sample? (6 pts)
(b) The energy needed to remove one electron from a gaseous potassium atom is only about two-thirds
as much as that needed to remove one electron from a gaseous calcium atom, yet nearly three times as
much energy as that needed to remove one electron from K+
as from Ca+
. 1) What explanation can you
give for this difference? 2) Next, compare the ionization energy of Ca+ with that of neutral K (4 pts)

4. (10 points)
Consider an electron confined in a box with infinite potential barriers (particle in a box). If the energy
difference between the ground state (n=1) and the first excited state (n=2) corresponds to the absorption
of light with a wavelength of either 800 nm or 400 nm (1 nm = 10−9 m), determine the length of the
box in each case. Express your answers in angstroms (1 Å = 10−10 m).

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