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Version 001 – HW08-Wavefunctions – sparks – (52100)
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Mlib 02 0095
001 10.0 points
Which of the following provided evidence that
the electrons in atoms are arranged in distinct
energy levels?
1. the results of the Millikan oil-drop experiment
2. the existence of elements with noninteger
values for atomic weights
3. the scattering of α particles by a metal
foil
4. the deflection of ions in a mass spectrometer
5. the observation of line spectra from gas
discharge tubes correct
Explanation:
The fact that gases emitted only specific
wavelengths of energy suggested that electron
energy states are quantized.
AtomicSpec 01
002 10.0 points
Assume n1 and n2 are two adjacent energy
levels of an atom. The emission of radiation
with the longest wavelength would occur for
which two values of n1 and n2 ?
1. 2,1
7. 3,2
Explanation:
The frequency of a photon emitted when
an electron moves between levels n1 and n2 is
given by the Rydberg equation:
1
1
ν=R
− 2
2
n1 n2
A
B
C
5. 7,6
6. 8,7 correct
,
Wavefunctions 1s 01
003 10.0 points
The graph shows the radial distribution plots
for the 1s wavefunctions for H, He, and He+ .
4πr 2 Ψ2
4. 4,3
where R = 3.29 × 1015 Hz. The emission of
radiation with the longest wavelength corresponds to that with the smallest frequency.
From inspection of the formula above we see
that ν is smallest when n1 = 8 and n2 = 7.
Conceptual
E = hν =
Solution:
1
1
hR
−
gives the energy of the phon21 n22
tons emitted. The emission of radiation with
the longest wavelength corresponds to photons with the smallest energy. From the Bohr
frequency condition the energy of the emitted photon must be equal to the difference
in energy between the higher and lower levels. An energy level diagram for the H-atom
shows that as the energy levels get higher, the
gaps between them converge; of the transitions listed, the two adjacent levels which are
the closest together are n1 = 8 and n2 = 7.
Thus a transition from n1 = 8 to n2 = 7
will result in the emission of a photon with
the smallest energy, hence the longest wavelength.
2. 6,5
3. 5,4
1
radius
Version 001 – HW08-Wavefunctions – sparks – (52100)
Which plot is the 1s wavefunction for the He+
ion?
1. C
2. There is no way to know
3. B
4. A correct
Explanation:
H has one electron and one proton. He has
two electrons and two protons. He+ has one
electron and two protons. Therefore the electron will have the greatest attraction to the
the nuclei with two protons. In He there will
be a slight reduction in the effective nuclear
charge due to the electron-electron repulsion.
In He+ , there is only one electron so the radius
will be the smallest. Plot A is peaked closest
to the nucleus so it will be the smallest.
ChemPrin3e 01 53 54
004 10.0 points
How many electrons can have the quantum
numbers n = 2; ℓ = 1 in an atom?
1. 4
2
To find the maximum number of electrons
that can have the stated values of n and ℓ
(and any allowed value of mℓ and ms ), double
the number of different values of mℓ .
If only n is stated then all allowed values of
ℓ, mℓ and ms are possible; each value of ℓ will
have its own set of values of mℓ . Total each of
these sets of values and then multiply by two
to get the number of electrons.
If n , ℓ and mℓ are stated then the only other
variable is ms which has only two values (only
two electrons may share n , ℓ and mℓ ).
ChemPrin3e T01 39
005 10.0 points
The three quantum numbers for an electron in
a hydrogen atom in a certain state are n = 4,
ℓ = 2, mℓ = 1. The electron is located in
what type of orbital?
1. 4s
2. 3p
3. 4p
4. 4d correct
5. 3d
2. 6 correct
Explanation:
The notation is nℓ , where
n = 1, 2, 3, 4, 5, ..., ℓ = 0, 1, 2, ..., (n − 1)
represented as a letter:
3. 3
4. 7
5. 5
Explanation:
The notation is nℓ where
n = 1, 2, 3, 4, 5, · · ·
ℓ = 0, 1, 2, · · · , (n − 1) represented by a letter:
ℓ value
letter
0
s
1
p
2
d
3
f
4
g
5
h
mℓ = −ℓ, −(ℓ − 1), −(ℓ − 2), · · · , 0, · · ·
+(ℓ − 2), +(ℓ − 1), +ℓ
1
and ms = ± .
2
ℓ
0
orbital s
1 2
p d
3
f
4
g
5 etc.
h
and
mℓ
=
−ℓ, −(ℓ − 1), −(ℓ −
2), ..., 0, ..., +(ℓ − 2), +(ℓ − 1), ℓ.
The value of mℓ is not needed to determine
the orbital type, as long as it is valid.