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WEEK 2: 16 JAN THRU 22 JAN; LECTURES 5-6
Learning Objectives
Interpretation of Line spectrum
(What is happening that causes the emission lines?)
Know that quantized emissions represent energy transitions
Be able to interpret line spectra by assigning lines to transitions
Connect line spectra to the energy of emitted photons, the color of light emitted, and its wavelength
Bohr Model of the hydrogen atom: where is the electron in the H atom?
Qualitative Goals:
Connect the line spectrum of hydrogen to the energy level diagram of hydrogen using the Bohr model.
Define and describe the energy of an electron in the hydrogen atom
+
Connect emission and absorption to pictures of electrons in orbit; We are using He ion for this goal
Have a qualitative ability to describe emission and absorption using the principal quantum number.
Know the sign of the energy change (positive or negative) when emission or absorption occurs.
Quantitative Goals
Calculate E given ni and nf (Calculate energy of emitted photon.)
+
Calculate ionization energy for H atom or He (knowing that n = for ionization)
Know that the energy change is negative if the photon is emitted.
Orbitals: Solutions to Schrödinger equation
What is meant by the “electron density” (or the probability of finding an electron)?
Know the qualitative meaning of wavefunctions, which are solutions to the Schrödinger Equation.
Describe the meaning of probability density, and electron density as the location of an electron.
Quantum Numbers
Be familiar with the names of principle, angular, and magnetic quantum numbers
Define shell, subshell and orbital
Know and follow rules for allowed combination of quantum numbers
Understand the relationship between quantum numbers and size, shape, and orientation of an orbital
Know orbital names.
Describe the value of electron density in regions of space using electron density plots or contour diagrams
Interpret an electron density plot, and define nodes and lobes of orbitals
Make connections between electron configuration and orbitals; know that quantum numbers describe orbitals, and
orbitals sufficiently describe the location of the electron
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WEEK 2: 16 JAN THRU 22 JAN; LECTURES 5-6
Homework Problems
Due: Thurs. Jan 24
1. The brightest emission line in the line spectrum of potassium is at 535nm. What is the energy of
the photon emitted?
2. The brightest emission line of an element is 420nm. What is the color of the flame?
3. In the Bohr model for the hydrogen atom, in which orbit does an electron have higher overall
energy: n = 1 or n = 5?
4. What is the maximum number of electrons that can have n = 3 and ms = + ½?
5. How many possible orbitals are there with n = 3 and m = 1?
6. Give the set of quantum numbers that describes each of the following orbitals assuming they are
all in the third shell.
A.
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B.
C.
D.
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WEEK 2: 16 JAN THRU 22 JAN; LECTURES 5-6
7. If the Bohr model is used, what frequency of light
would be required for ionization of hydrogen?
A.
B.
C.
D.
E.
10. Which of the following statements is/are true
for the Bohr model of the hydrogen atom?
14
6.17 10 Hz
3
1.31 10 Hz
15
3.29 10 Hz
10
4.31 10 Hz
None of the above is within 5% of the
correct answer
1.
2.
3.
8.
Which of the following electron transitions in a
hydrogen atom results in the greatest release of
energy from the atom?
A.
B.
C.
D.
E.
A.
B.
C.
D.
E.
n = 3 to n = 4
n = 1 to n = 3
n = 6 to n = 4
n = 7 to n = 5
n = 2 to n = 5
9. Which of the following transitions in a hydrogen
atom results in emission of light?
i.
ii.
iii.
iv.
v.
A.
B.
C.
D.
E.
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n=3
n=1
n=6
n=7
n=2
iii only
i and ii only
ii and iii only
iii and iv only
i, ii, and v
The radius of the orbit increases as the
principal quantum number increases.
The energy required to ionize the atom
increases as the principal quantum
number decreases.
Light emitted by the excited hydrogen
atom corresponds to transitions from
orbits of higher principal quantum
number to lower principal quantum
number.
1 only
1and 2 only
2 and 3 only
1 and 3 only
1, 2, and 3
11. For electron distributions, which of the following
statements is/are true?
1.
2.
to n = 4
to n = 3
to n = 4
to n = 5
to n = 5
3.
A.
B.
C.
D.
E.
d orbitals have a spherical shape.
p orbitals have a high electron density at
the nucleus.
s orbitals have no electron density at the
nucleus.
1 and 2
2 only
2 and 3
3 only
None of the statements is true
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WEEK 2: 16 JAN THRU 22 JAN; LECTURES 5-6
Recitation Worksheet
-----------------------------------------------------------------------------------------------------------------------1. (A) What is the wavelength of one X-ray photon if the frequency is 1.00 × 1019 s−1?
(B) What is the energy of one X-ray photon of this frequency?
(C) What is the energy of one mole of X-ray photons of the same wavelength?
-----------------------------------------------------------------------------------------------------------------------2. A sodium vapor street lamp emits yellow light at wavelength λ = 589 nm. How much energy
is released if a mole of photons are emitted?
A.
B.
C.
D.
E.
2.0
5.4
7.2
1.9
3.5
105 J
108 J
10–13 J
10–4 J
10–19 J
HINT 1: What is the relationship needed to find the energy of a single photon?
HINT 2: How many photons are in a mole of photons?
-----------------------------------------------------------------------------------------------------------------------3. There is a red emission line at 670nm in the line spectrum of Li. What is the energy difference
between the energy levels involved in the electronic transition that produces this emission
line?
A.
B.
C.
D.
2.97
6.70
4.48
9.89
10–19 J
10–7 J
1014 J
10–28 J
--------------------------------------------------------------------------------------------------------------------4A. An emission line the hydrogen atom has a wavelength of 93.8 nm. What region in the
electromagnetic spectrum is this emission found?
4B. Determine the final value of n associated with this emission? (Hint: Consider E = h and
the Rydberg equation, use this to find the value of nf.)
4C. Determine the initial value of n associated with this emission. (Hint: Will this value be
higher or lower than nf and why is this the case? What equation will you use to determine
this value; what values do you know?)
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WEEK 2: 16 JAN THRU 22 JAN; LECTURES 5-6
-----------------------------------------------------------------------------------------------------------------------5A. Which of the following electron transitions in a hydrogen atom will emit a photon, which
absorb a photon? (How do you know?)
A. n = 1 to n = 3
B. n = 4 to n = 3
C. n = 3 to n = 2
D. n = 3 to n = 1
E. n = 2 to n = 3
5B. Which of the above electron transitions in a hydrogen atom will result in emission of light
with the longest wavelength?
-----------------------------------------------------------------------------------------------------------------------6A. Use the Bohr model and determine the wavelength of light that would ionize a hydrogen
atom. (Hint: ionization is the removal of an electron; assume we are removing it from the n
= 1 value)
6B. If the electron were in an excited state (n =3) what would the ionization energy be?
-----------------------------------------------------------------------------------------------------------------------7. Consider the rules for assigning quantum numbers.
Which is not a permissible set of quantum numbers?
Identify the orbital (if possible)
a)
n = 2, ℓ = 0, mℓ = 0
_____
b)
n = 3, ℓ = 2, mℓ = 2
_____
_____
c)
n = 2, ℓ = 1, mℓ = 1
d)
n = 3, ℓ = 3, mℓ = 0
_____
_____
e)
n = 4, ℓ = 3, mℓ = 3
Hint: What quantum number(s) gives the electron shell?
What quantum number number(s) indicate the subshell?
Which quantum number(s) define the orbitals in a subshell?
------------------------------------------------------------------------------------------------------------------------8. Which of the following represents an orbital in which a 3d electron could be found?
A.
B.
C.
D.
E.
1 only
2 only
4 only
1 and 5
2 and 3
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