2017 Spring Semester Quiz 2
For General Chemistry I (CH101)
Date: Apr 3 (Mon),
Professor Name
Time: 19:00 ~ 19:45
Class
Student I.D. Number
Name
----------------------------------------------------------------------------------------------------------------------------------------
Use the following constants to solve problems.
(Planck constant 𝒉 = 6.626 × 10-34 J s)
(Mass of electron 𝒎𝒆 = 9.109 × 10-31
kg)
(Permittivity of the vacuum 𝜺𝟎 = 8.854 × 10-12 C2 J-1 m-1)
(Charge of the electron 𝒆 = 1.602 × 1019
C)
(Avogadro’s number 𝑵𝑨 = 6.022 × 1023 mol-1) (Ratio of a circle's circumference to its diameter 𝝅 =
3.14)
(Speed of light c = 𝟐. 𝟗𝟗𝟖 × 108 m s-1
(Bohr radius 𝒂𝟎 =
(1 Rydberg =
𝜺𝟎 𝒉𝟐
𝝅𝒆𝟐 𝒎𝒆
𝒆𝟒 𝒎𝒆
𝟐
𝟖𝜺𝟐
𝟎𝒉
= 2.18 × 10-18 J)
= 𝟎. 𝟓𝟐𝟗 × 10-10 m)
----------------------------------------------------------------------------------------------------------------------------------------
1. (Total 8 pts, each 2 pts) Read the following statements or equations, and verify whether these
are “TRUE (T)” or “FALSE (F)”. (2 pts for a right answer, -2 pts for a wrong answer, 0 pt for no answer)
(a) The probability for locating an electron in the volume element 𝒅𝑽 = 𝒓𝟐 𝐬𝐢𝐧 𝜽 𝒅𝒓𝒅𝜽𝒅𝝓 when
the electron is in the specific quantum state (𝒏, 𝒍, 𝒎) is given by
(𝝍𝒏𝒍𝒎 )𝟐 𝒅𝑽 = [𝑹𝒏𝒍 (𝒓)]𝟐 [𝒀𝒍𝒎 (𝜽, 𝝓)]𝟐 𝒅𝑽
Answer:
T
(b) Hartree atomic orbitals are the exact solutions of Schrodinger equation for many-electron
atoms.
Answer:
F
(c) Among four quantum numbers (𝒏, 𝒍, 𝒎, 𝒎𝒔 ), the energy levels of electron in one-electron
atoms depend only on the principal quantum number n.
Answer:
T
(d) The Pauli exclusion principle states that no two electrons in an atom can have the same set
of four quantum numbers (𝒏, 𝒍, 𝒎, 𝒎𝒔 )
Answer:
T
2. (Total 10 pts) Here is a wave function of one-electron atoms.
𝟑
𝝍𝒏𝒍𝒎 (𝒓, 𝜽, 𝝓) =
𝟏
𝒁 𝟐
𝟓𝟏𝟐√𝟓𝝅 𝒂𝟎
𝝈
𝒁𝒓
𝟒
𝒂𝟎
( ) 𝝈(𝟖𝟎 − 𝟐𝟎𝝈 + 𝝈𝟐 )𝒆𝒙𝒑 (− ) 𝐜𝐨𝐬 𝜽, 𝝈 =
(a) (3 pts) Find the values of 3 quantum numbers 𝒏, 𝒍, and 𝒎.
각 number당 1점, 부분점수 없음
n: 4
------ +1 pt
l: 1
------ +1 pt
m: 0
------ +1 pt
(b) (2 pts) How many the number of radial nodes and angular nodes does 𝝍𝒏𝒍𝒎 (𝒓, 𝜽, 𝝓) have?
각각의 노드당 1점, 부분점수 없음
# of Radial node: 2
------ +1 pt
# of Angular node: 1
------ +1 pt
(c) (3 pts) For existed nodes in this given wave function, find the conditions of variants for each
nodes. Suppose that this atom is Hydrogen (𝒁 = 1).
[Boundary condition: 𝟎 ≤ 𝐫 < ∞, 𝟎 ≤ 𝜽 ≤ 𝝅, 𝟎 ≤ 𝝓 ≤ 𝟐𝝅]
2 radial nodes-> 𝝈(𝟖𝟎 − 𝟐𝟎𝝈 + 𝝈𝟐 ) = 𝟎
r = (𝟏𝟎 ± 𝟐√𝟓 )𝒂𝟎 or r = 5.53𝒂𝟎 , 14.47𝒂𝟎
------ +1 pt
---------------------------------------- +1 pt(하나당 0.5 pt)
r = 0 쓰면 감점 [𝝈 = 𝟎(not a root for radial node)]
--------------- -0.5 pt
1 angular node-> 𝐜𝐨𝐬 𝜽 = 𝟎
--------------- +0.5 pt
𝜽 = 𝝅/2
--------------- +0.5 pt
(d) (2 pts) Which orbital does 𝝍𝒏𝒍𝒎 (𝒓, 𝜽, 𝝓) represents?
답 +2 pts, 부분점수 없음
4pz
--------------- +2 pts
3. (Total 8 pts) The wave function of an electron in the lowest (that is, ground) state of the
hydrogen-like He+ atom is
𝟏
𝟑𝟐 𝟐
𝟐𝒓
𝟏
𝒂𝟎
𝒂𝟎
𝟒𝝅
𝝍(𝒓) = 𝑹𝒏𝒍 (𝒓) ∙ 𝒀𝒍𝒎 (𝜽, 𝝓) = {( 𝟑 ) 𝒆𝒙𝒑 (− )} ∙ ( )
𝟏/𝟐
, 𝒂𝟎 = 𝟎. 𝟓𝟐𝟗 × 𝟏𝟎−𝟏𝟎 𝒎,
(with the assumption that μ ≈ 𝒎𝒆 )
(a) (4 pts) In this wave function, calculate the distance 𝒓𝒎𝒂𝒙 from the nucleus to the location that
the radial probability density is the largest. Express your answers in meter.
(Hint: radial probability density: 𝒓𝟐 [𝑹𝒏𝒍 (𝒓)]𝟐 )
--- 미분값이 0일때
값이 최대라는 식
적으면 + 1 pt
--- 답 +3 pts
(b) (2 pts) Estimate the energy, and 𝒓̅𝒏𝒍 (average distance of the electron from the nucleus) of
given wave function. Express your
answers in Rydberg or Joule for
energy, and meter for distance.
---
E식 +0.5 pt
---
E답 +0.5 pt
---
r식 +0.5 pt
---
r답 +0.5 pt
(c) (2 pts) Estimate the energy, and 𝒓̅𝒏𝒍 of the 1s orbital of neutral He atom. The effective nuclear
charge for He is 𝒁𝒆𝒇𝒇 (𝟏) = 𝟏. 𝟔𝟗. Express your answers in Rydberg or Joule for energy, and meter
for distance.
- E식+0.5 pt
-E답+0.5 pt
- r식 +0.5 pt
- r답+0.5 pt
4. (Total 8 pts) Photoelectron spectroscopy studies of sodium atoms (Na, atomic number = 11)
excited by X-rays with wavelength 9.890 x 10-10 m show four peaks in which the electrons have
speeds 7.9924 x 106 m/s, 2.0421 x 107 m/s, 2.0712 x 107 m/s, and 2.0956 x 107 m/s.
(a) (4 pts) Calculate the ionization energy of the electrons in each peak. Express your answer in
kJ/mol.
- 식 +1 pt
- 식 +1 pt
-각
피크
IE당 +0.5 pt
(b) (4 pts) Assign each peak to an orbital of the sodium atom.
각 피크당 + 1 pt. 피크의 전자속도와 그에 맞는 오비탈이 일치해야만 정답, 부분점수 없음
Peak 1(ve = 7.9924 x 106 m/s) = 1s
------ +1 pt
Peak 2(ve = 2.0421 x 107 m/s) = 2s
------ +1 pt
Peak 3(ve = 2.0712 x 107 m/s) = 2p
------ +1 pt
Peak 4(ve = 2.0956 x 107 m/s) = 3s
------ +1 pt
5. (Total 6 pts) Consider following ions; Be+, C-, Ne2+, P2+, Cl-, and As+.
(Atomic number- Be: 4, C: 6, Ne: 10, P: 15, Cl: 17, As: 33)
(a) (3 pts) Write ground-state electron configurations for listed 6 ions.
각 이온당 0.5 pt, 부분점수 없음
(b) (3 pts) Among them, choose the ion(s) expected to be paramagnetic due to the presence of
unpaired electrons.
Be+, C-. Ne2+, P2+, As+
----
각 이온당 0.6 pt, 부분점수 없음