PRACTICE PROBLEMS Atomic Structure
Isotope problems:
1. Calculate the average atomic mass of an element whose two isotopes naturally occur
in the following proportions and have the following atomic masses:
2. Sulfur has two isotopes, 32S, which is 98.00% of the sulfur and 35S, which is 2.00% of
the sulfur. What is atomic mass of sulfur?
3. Find the atomic mass of hafnium, element # 72. 5% of the atoms have mass 176, 19%
have mass 177, 27% of the atoms have mass 178, 14% have mass 179, and 35% have
mass 180.0.
4. Suppose a new element, Q, is discovered. Researchers find that this element has two
isotopes. In a scientific journal, the two isotopes are described as having atomic
numbers of 110 and 111. What is wrong with this description?
5. This type of problem would appear ONLY as a bonus question (extra points).
Phosphorus has two isotopes, 32P and 30P. The experimentally determined mass of phosphorus is
30.97376g/mol. What are the percentages of the two isotopes?
Energy/Wavelength Problems:
6.
When copper ions are placed in a flame they emit a characteristic green flame
color with a wavelength () of 490 nm. Calculate the average energy (∆E)
corresponding to the observed flame color.
[ h = Planck’s constant = 6.626 x 10-34 J·sec
hint: be sure to convert nm to m!
7.
c = speed of light = 2.998 x 108 m/sec ]
When lithium ions are placed in a flame they emit a characteristic red flame color
with a wavelength () of 671 nm. Calculate the average energy (∆E) corresponding
to the observed flame color.
[ h = Planck’s constant = 6.626 x 10-34 J·sec
hint: be sure to convert nm to m!
c = speed of light = 2.998 x 108 m/sec ]
8. Sally is trying to use a flame test to identify an unknown. She knows the unknown
ONE of the following metal ions: lithium, sodium, or potassium ions.
(a) What would she do to identify the unknown?
Describe the specific technique, what she would observe, and how she would know which unknown she had.
(b) Describe what is happening inside the atoms in a flame test.
9.
This type of problem would appear ONLY as a bonus question (extra points)
The amount of energy associated with the transition of an electron from n=4 to n=2
is 4.09 x 10-19 J.
(a) Calculate the wavelength (λ) corresponding to this transition.
(b) Indicate whether the radiation given off would be visible, infrared, or ultraviolet
and explain how you know.
Bohr Model Problems:
10.
Draw a Bohr model of an atom of sulfur (S)
11.
Draw a Bohr model of an atom of magnesium (Mg)
Electron Configuration Problems:
1s2|2s22p6|3s23p6|4s23d104p6|5s24d105p6|6s24f145d106p6|7s25f146d107p6
[He]
[Ne]
[Ar]
[Kr]
[Xe]
12.a. Write the electron configurations for tin (Sn):
b. Write the electron configurations for francium (Fr):
c. What element has the following electron configuration?
1s22s22p63s23p64s23d104p65s24d105p4
d. What element has the following electron configuration?
[Xe]6s24f145d8
[Rn]
PRACTICE PROBLEMS Atomic Structure – ANSWER KEY
1. Calculate the average atomic mass of an element whose two isotopes naturally occur
in the following proportions and have the following atomic masses:
25% Isotope 1, atomic mass 64.9 amu
75% Isotope 2, atomic mass 67.1 amu
mass of element = (relative abundance of isotope 1)(mass of isotope 1) + (percent of 32S)(mass of 32S)
mass of element = (0.25 x 64.9) + (0.75 x 67.1)
= 65.5 amu
2. Sulfur has two isotopes, 32S, which is 98.00% of the sulfur and 35S, which is 2.00% of
the sulfur. What is atomic mass of sulfur?
Equation 1:
mass of sulfur = (percent of 35S)(mass of 35S) + (percent of 32S)(mass of 32S)
percent of 32S = 98.00% = 0.9800
mass of 32S = 32.00
percent of 35S = 2.00% = 0.0200
mass 35S = 35.00
Substituting into equation 1 we get:
mass of sulfur = (0.0200)(35.00) + (0.9800)(32.00)
= 0.700 + 31.36
= 32.06 amu
3. Find the atomic mass of hafnium, element # 72. 5% of the atoms have mass 176, 19%
have mass 177, 27% of the atoms have mass 178, 14% have mass 179, and 35% have
mass 180.0.
Equation 1:
mass of hafnium =
(rel abundance of Hf-176 x mass of Hf-176) + (rel abundance of Hf-177 x mass of Hf-177) +
(rel abundance of Hf-178 x mass of Hf-178) + (rel abundance of Hf-179 x mass of Hf-179) +
(rel abundance of Hf-180 x mass of Hf-180)
mass of hafnium = (0.05 x 176) + (0.19 x 177) + (0.27 x 178) + (0.14 x 179) + (0.35 x 180) = 18.55 amu
4.
Suppose a new element, Q, is discovered. Researchers find that this element has two
isotopes. In a scientific journal, the two isotopes are described as having atomic
numbers of 110 and 111. What is wrong with this description?
Isotopes have the same atomic number…. Their mass number is what changes… due to different
numbers of neutrons… This journal entry as written is describing two different elements.
5.
This type of problem would appear ONLY as a bonus question (extra points).
Phosphorus has two isotopes, 32P and 30P. The experimentally determined mass of phosphorus is
30.97376g/mol. What are the percentages of the two isotopes?
The mass of phosphorus is a weighted average of the masses of the isotopes. That is:
Mass of phosphorus = (percent of 32P)(mass of 32P) + (percent of 30P)(mass of 30P)
The mass of each isotope is determined by its mass number.
mass of 32P = 32.00 amu
mass of 30P = 30.00 amu
The sum of the percentages is equal to one so:
let x = percentage of 32P
and 1-x = percentage of 30P
If we substitute into equation 1, we get the following:
30.97376 = x(32.00) + (1-x)30.00
from here it is algebra and we solve it as follows:
30.97376 = 32.00x + 30.00 - 30.00x
30.97376 - 30.00 = 32.00x - 30.00x
0.97 = 2.00x
x = 0.49; 1- x = 0.51
therefore, x = percent 32P = 49%
and 1-x = percent 30P = 51%
6. When copper ions are placed in a flame they emit a characteristic green flame color
with a wavelength () of 490 nm. Calculate the average energy (∆E) corresponding to
the observed flame color.
[ h = Planck’s constant = 6.626 x 10-34 J·sec
hint: be sure to convert nm to m!
490 nm x 1 x 10-9 m / 1 nm = 4.90 x 10-7 m
c = speed of light = 2.998 x 108 m/sec ]
E = hc/ = (6.626 x 10-34 J·sec) x (2.998 x 108 m/sec) = 4.05 x 10-19 J
4.90 x 10-7 m
7. When lithium ions are placed in a flame they emit a characteristic red flame color
with a wavelength () of 671 nm. Calculate the average energy (∆E) corresponding to
the observed flame color.
[ h = Planck’s constant = 6.626 x 10-34 J·sec
hint: be sure to convert nm to m!
c = speed of light = 2.998 x 108 m/sec ]
671 nm x 1 x 10-9 m / 1 nm = 6.71 x 10-7 m
E = hc/ = (6.626 x 10-34 J·sec) x (2.998 x 108 m/sec) = 2.96 x 10-19 J
6.71 x 10-7 m
8. Sally is trying to use a flame test to identify an unknown. She knows the unknown
ONE of the following metal ions: lithium, sodium, or potassium ions.
(b) What would she do to identify the unknown?
Describe the specific technique, what she would observe, and how she would know which unknown she had.
Sally would take a wood splint that had been soaked in water and place the tip of it in a jar on the
unknown, picking up some of the crystals. Then she would place that same end of the wood splint in the
flame of a Bunsen burner…. And observe the color of the flame.
If the flame was red, she would know the unknown was lithium. If the unknown was yellow, she would
know the unknown was sodium. If the unknown was purple, she would know the unknown was
potassium.
(b) Describe what is happening inside the atoms in a flame test.
Excited electrons give off energy in the form of light (photons) as they move back to their ground state.
The photons have a very specific wavelength that corresponds to a color on the visible light spectrum.
9. This type of problem would appear ONLY as a bonus question (extra points)
The amount of energy associated with the transition of an electron from n=4 to n=2
is 4.09 x 10-19 J.
(a) Calculate the wavelength (λ) corresponding to this transition.
E = hc/ = (6.626 x 10-34 J·sec) x (2.998 x 108 m/sec) = 4.09 x 10-19 J
X
X = 4.85 x 10-7 m = 485 nm
(b) Indicate whether the radiation given off would be visible, infrared, or ultraviolet
and explain how you know.
This wavelength is fairly short and within the visible range… which goes from
~400nm to 700 nm.
Bohr Model Problems:
10.
Draw a Bohr model of an atom of sulfur (S)
11.
Draw a Bohr model of an atom of magnesium (Mg)
12.a. Write the electron configurations for tin (Sn):
1s22s22p63s23p64s23d104p65s24d1052
Or
[Kr] 5s24d1052
b. Write the electron configurations for francium (Fr):
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p67s1
Or
[Rn] 7s1
c. What element has the following electron configuration?
Te (tellurium)
1s22s22p63s23p64s23d104p65s24d105p4
d. What element has the following electron configuration? Pt (platinum)
[Xe]6s24f145d8