The Structure of Atoms

Physical constants: h = 6.626 x 10^-34 Joule-sec; c = 3.00 x 10⁸ m/s; mass of electron = 9.1 x 10^-31 kg

Question 1.

Which of the following statements is correct for an electron that has the quantum numbers n = 4 and m_l = -2?
a) the electron may be in a p orbital

b) none of the above applies to this electron

c) the electron may be in a d orbital

d) the electron is in the second principal shell

e) the electron must have a spin quantum number m_s = + 1/2

Question 2.

Four electrons in an atom have the quantum number given below. Which electron is at the lowest energy?

a) l = -1, m_s = - 1/2" a) n = 3, l = 1, m_l = -1, m_s = - 1/2

b) l = 0, m_s = + 1/2" b) n = 3, l = 2, m_l = 0, m_s = + 1/2

c) l = 0, m_s = + 1/2" c) n = 4, l = 0, m_l = 0, m_s = + 1/2
d) l = 0, m_s = - 1/2" d) n = 3, l = 0, m_l = 0, m_s = - 1/2

Question 3.

For an electron that has quantum numbers n = 4 and m_l = 0, which of the following is true?
a) it must have the quantum number n = 0

b) it may have the quantum numbers, l = 0, 1, 2, 3

c) it must have the quantum number l = 0

d) it must have the quantum number ms = + 1/2

Question 4.

What type of orbital is occupied by an electron with the quantum numbers n = 5, l = 3. How many orbitals of this type are found in a multielectron atom?

a) 5p, 6

b) 5p, 3

c) 5d, 2

d) 5f, 14

e) 5f, 7

Question 5.

Identify the subshell in which electrons with the quantum numbers n = 6, l = 1 may be found.

a) 3d

b) 6p

c) 6d

d) 5p

e) 6f

Question 6.

Identify the subshell in which electrons with the quantum number n = 5, l = 4 are found.

a) 5p

b) 5g

c) 4f

d) 5d

e) 5f

Question 7.

Which of the following sets of quantum numbers is not allowed?

a) n = 2, l = 0, ml = 0

b) n = 3, l = 2, ml = -3

c) n = 2, l = l, ml = 0

d) n = 3, l = 1, ml = -1

Question 8.

Which of the following sets of quantum numbers are allowed for an electron in an atom?

n l ml ms

1) 2 1 0 +1/2

2) 3 0 +1 -1/2

3) 3 2 -2 -1/2

4) 1 1 0 +1/2

5) 2 1 0 0

a) 2, 4, 5

b) 1, 2, 3

c) 3, 4

d) 2, 4

e) 1, 3

Question 9.

Which of the following sets of quantum numbers is not allowed?

a) n = 3, l = 0, ml = 0

b) n = 3, l = 1, ml = -1

c) n = 2, l = 2, ml = -1

d) n = 2, l = l, ml = 0

Question 10.

What is the total number of orbitals in the n = 2 level?

a) 8

b) 2

c) 4

d) 3

e) 10

Question 11.

Which in the following list of atomic orbital designations are possible? 6p 4g 3f 8s 2d

a) 4p, 3f & 2d

b) 6p & 8s

c) 3f & 2d

d) only 6p

e) only 8s

Question 12.

The subshell that arises after f is called the g subshell. How many g orbitals are present in the g subshell?

a) 14

b) 9

c) 7

d) 15

e) 5

Question 13

Consider the following historical statements:

I. The Millikan "oil drop" experiment was able to determine the charge of an electron.
II. Rutherford's "gold foil experiment" established the nuclear atom concept.
III. Thomson determined the charge to mass ratio of electrons in his cathode ray tube experiments.

a) I and II are correct but III is false.
b) II and III are correct but I is false.
c) I and III are correct but II is false.
d) All are correct.

Question 14

Identify the INCORRECT statement regarding the gold foil experiment:

a) A few particles rebounded as if hitting very dense positive charges in the foil.
b) Most particles bounced back from the gold foil.
c) Most particles passed through the foil as if through empty space.
d) The gold foil was bombarded with positively charged alpha particles, having a mass four times that of a proton.

Question 15

Identify the INCORRECT statement below:

a) The mass number of an atom is the number of neutrons plus protons in the atom.
b) The neutron has nearly the same mass as the proton but zero charge.
c) Two elements differ from one another by having a differing mass number.
d) Atomic number is the number of protons in the nucleus of an atom.
e) The mass of the electrons is a small fraction of the total mass of any atom.

Question 16

The element Fluorine has only one really stable isotope. What is the composition of its nucleus?

a) 19 protons
b) 9 protons and 19 neutrons
c) 9 protons and 10 neutrons
d) 10 protons and 9 neutrons

Question 17

A neutral atom of the ²³⁵U isotope has how many protons, neutrons, and electrons?

a) 92 p, 143 n, 92 e
b) 235 p, 235 n, 235 e
c) 92 p, 92 n, 92 e
d) 92 p, 235 n, 92 e

Question 18

What is the wavelength in meters of microwave radiation, having a typical frequency of 3 x 10⁹ Hz?

a) 9 x 10^-17 m
b) 9 x 10¹⁷ m
c) 10 m
d) 0.1 m

Question 19

What is the energy in Joules of a mole of photons of microwave light having a frequency typical of microwave? (frequency = 3.0 x 10⁹ Hz). (A Joule is enough energy to raise the temperature of 1 gram of water about a quarter of a degree Celsius.)

a) 1.2 x 10²³ J
b) 1.98 x 10^-24 J
c) 1.2 J
d) 1.98 x 10^-34 J

Question 20

Rank the following types of radiation from highest energy to lowest:

ultraviolet / visible / xray / microwave / infrared

a) xray, ultraviolet, microwave, infrared, visible
b) ultraviolet, xray, visible, infrared, microwave
c) infrared, microwave, ultraviolet, visible, xray
d) xray, ultraviolet, infrared, visible, microwave
e) xray, ultraviolet, visible, infrared, microwave

Question 21

An excited Hydrogen atom in the n=3 energy level decays to the n=2 energy level and emits a photon of light. If the energies of these two levels are separated by 3.029 x 10^-19 J, what will be the wavelength of the light emitted in nanometers?

a) 656 nm
b) 484 nm
c) 1073 nm
d) 1.07 x 10^-19 nm
e) 3.3 x 10^-10 nm

Question 22

According to the deBroglie equation, the characteristic wavelength of an electron moving around an atomic nucleus will be:

a) about the size of the nucleus.
b) about the same size as the atom.
c) large compared to the atomic scale.
d) immeasurably small compared to any dimensions we care about.

Question 23

Identify the INCORRECTstatement below:

a) The total number of electrons required to fill the n=1 level is 2.
b) The total number of electrons that can have n=2 in a many-electron atom is 8.
c) The total number of electrons that can occupy an atomic orbital is 2.
d) The total number of electrons that can "fit" in the 3d sublevel is 5.

Question 24

Which of the following full notations for the electron state is consistent with the last electron added in forming the electron configuration of Scandium (Sc)?

a) (3, 2, 1, +1/2)
b) (4, 0, 0, +1/2)
c) (4, 2, 0, +1/2)
d) (4, 2, 1, +1/2)

Question 25

Fill in the blank: The l quantum number tells which sublevel the electron is in and most directly specifies the _______ of the atomic orbital.

a) orientation
b) size
c) energy
d) shape

Question 26

The statement that no two electrons can have the same set of four quantum numbers in any atom is a consequence of:

a) The Aufbau Principle.
b) The Heisenberg Uncertainty Principle.
c) The Pauli Exclusion Principle.
d) Hund's Rule.

Question 27

Which is the following is an INCORRECT electron configuration?

a) Ti = [Ar]4s²3d²
b) S = [Ne]2s²2p⁴
c) Li = 1s²2s¹
d) C = [He]2s²2p²

Practice Questions on the Atom and Atomic Spectra

1. Excited sodium atoms may emit radiation having a wavelength of 589 nm.
a) What is the wavelength in meters? b) What is the frequency of this light?
c) What region of the spectrum is this in? d) What is the energy of this light?

2. How does quantum theory explain the fact that excited potassium atoms emit light at only a relatively few wavelengths?

3. Draw the orbital diagrams for O and Si. How many unpaired electrons are in each of these?

4. Of the following electron configurations, state whether each represents an atom in the ground state, a possible excited state, or is incorrect.
a) 1s²2s²2p¹ b) 1s²2s¹3s¹ c) 1s²2s²2p⁶3s²2d² d) 1s²2s⁴2p² e) 1s¹2s¹

5. A radio station has a frequency of 96.5 MHz. Find the wavelength and E.

6. Microwaves have a frequency of around 2.5 GHz. What is the wavelength? (1 GHz = 10⁹ Hz)

7. What is the energy associated with 688 nm light? What color light is this?

8. A certain photon of radiation has energy of 4.65 x 10^-15 J. What is the wavelength of this light, in nm?

9. A certain light has an energy of 4.56 x 10^-19 J. What color is this light? (Hint: find wavelength in nm.)

Answers to select problems: 1a) 5.89 x 10^-7 m b) 5.09 x 10¹⁴ Hz d) 3.37 x 10^-19 J 5) wavelength = 3.11 m E=6.39 x 10^-26 J 6) 0.12 m 7) 2.89 x 10^-19 J, red 8) .0427 nm 9) violet (436 nm)

The Atom and Atomic Spectra Review Questions

1. An unknown substance has a mass of 3.44 grams and a volume of 2.77 mL. What is its density?

2. The density of dry air at 25 °C is 1.19 x 10^-3 g/cm³. What is the volume of 50.0 grams of air?

3. List the four main ideas of Dalton's atomic theory.

4. How were electrons discovered and by whom?

5. Describe Rutherford's gold foil experiment.

6. For the following elements, give the number of protons, electrons, and neutrons.
a) Ba b) Cu c) F

7. What is an isotope?

8. The four main isotopes of chromium have the following abundances: ⁵⁰Cr = 4.35% ,⁵²Cr = 83.79%, ⁵³Cr = 9.50%, ⁵⁴Cr =2.36%. What is the average atomic mass?

9. Chlorine has two main isotopes,³⁵Cl and ³⁷Cl. If the average atomic mass is 35.453, find the abundances of each isotope.

10. State the differences between the following atomic models: J.J. Thomson's, Rutherford's, Bohr's, Quantum mechanical model.

11. What is an atomic orbital?

12. What is the shape of an s orbital? a p orbital? How many electrons do each of these hold?

13. Define the Aufbau principle, Pauli exclusion principle, and Hund's rule.

14. Give the electron configuration for each of the following elements, both longhand and shorthand:
a) S b) Rb c) Au

15. Draw the electron configurations for: a) S b) Na c) B

16. List the colors in the visible spectrum from lowest wavelength to highest wavelength.

17. Explain where the different emission lines in the hydrogen spectrum come from.

18. What is the frequency of light whose wavelength is 5.66 x 10^-7 m?

19. What is the energy of light with a frequency of 7.22 x 10¹⁵Hz?

20. What is the energy of light with a wavelength of 4.22 x 10^-6 m?

21. Define ground state and excited state.

22. What is Heisenberg's uncertainty principle?

23. What was the main idea behind de Broglie's work?

24. What is the photoelectric effect? Give an example.

Frequency, Wavelength & The Speed of Light

1. What is meant by the "frequency of light"? What symbol is used for it, and what is the SI unit
for frequency?

2. Sketch a diagram of a wave and label its wavelength and its amplitude.

3. Give the equation that relates the wavelength and frequency of a light wave to the speed
of light.

4. What is the frequency in hertz of blue light having a wavelength of 425 nm?

5. Ozone protects the earth's inhabitants from the harmful effects of ultraviolet light arriving
from the sun. This shielding is a maximum for UV light having a wavelength of 295 nm.
What is the frequency in hertz of this particular wavelength of UV light?

6. Radar signals are also part of the electromagnetic spectrum in the microwave region. A
typical radar signal has a wavelength of 3.19 cm. What is the frequency in hertz?

7. FM radio dials are calibrated in frequency. In Ottawa, the radio station MAGIC 100
broadcasts its FM signal at a frequency of 101.1 megahertz (MHz). What is the wavelength
of this signal in meters?

8. Sodium vapour lamps are often used in residential street lighting. They give off a yellow light
having a frequency of 5.09 X 10¹⁴ Hz. What is the wavelength of this signal in nanometers?

9. AM radio dials are calibrated in frequency. A certain AM Brockville radio station broadcasts
at a frequency of 830 kHz. What is the wavelength of these radiowaves expressed in meters?

10. Some earthquake waves travel at 5 km/sec. What is the wavelength of these waves if the
earth tremors are 10 per second?

The Energy in a Light Wave

1. Sodium vapour lamps are used to sometimes light streets. If the frequency of the light coming
from them is 5.09 X 10¹⁴ Hz what is the energy in each photon?

2. What is the energy of each photon of red light that has a frequency of 4.0 X 10¹⁴ Hz?

3. Calculate the energy in joules/photon for green light having a wavelength of 550 nm.

4. Microwaves are used to heat food in microwave ovens. The microwave radiation is absorbed
by moisture in the food. This heats the water, and as water becomes hot, so does the food.
How many photons having a wavelength of 3.00 mm would have to be absorbed by 1.00 g of
water to raise its temperature by 1^oC?

5. The wavelengths of X-rays are much shorter than those of ultraviolet or visible light. Show
quantitatively why continued exposure to X-rays is more damaging than exposure to sunlight.

Periodicity and Atomic Structure

1. List the following types of electromagnetic radiation in order of increasing wavelength:

(i) the gamma rays produced by a radioactive nuclide used in medical imaging

(ii) radiation from an FM radio station at 93.1 MHz on the dial

(iii) a radio signal from an AM radio station at 680 kHz on the dial

(iv) the yellow light from sodium-vapor streetlights

(v) the red light of a light-emitting diode, such as in a calculator display

i < iv < v <iii < ii

i < iv <v < ii < iii

i < v < iv <ii < iii

iii < ii < v <iv < i

i < ii < iii <iv < v

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2. What is the frequency of radiation that has a wavelength of 0.589 pm?

5.09 x 1022 s-1

5.09 x 108 s-1

1.96 x 10-21 s-1

5.09 s-1

5.09 x 1020 s-1

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3. Is energy emitted or absorbed when the electronic transition from n = 3 to n = 6 occurs in hydrogen?

absorbed

emitted

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4. For the electronic transition from n = 3 to n = 8 in the hydrogen atom, calculate the energy.

2.08 x 10-19 J

1.05 x 10-16 J

3.41 x 10-20 J

2.42 x 10-19 J

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5. Calculate the energy of a photon with a frequency of 2.85 x 1012 s-1.

4.30 x 1045 J

6.97 x 10-38 J

2.32 x 10-46 J

1.89 x 10-21 J

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6. A diode laser of wavelength 785 nm is turned on for a period of 1.00 min. During that time it emits a signal with a total energy of 31.0 J. How many photons have been emitted?

1.22 x 1020

2.53 x 10-19

31.0

5.96 x 1040

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7. Neutron diffraction is an important technique for determining the structures of molecules. Calculate the velocity of a neutron that has a characteristic wavelength of 0.88 Å.

4.3 x 10-17 m s-1

4.5 x 1013 m s-1

2.2 x 10-4 m s-1

4.5 x 103 m s-1

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8. For n = 4, what are the possible values of l?

3, 2, 1

5, 4, 3, 2, 1, 0

4, 3, 2, 1

3, 2, 1, 0

4, 3, 2, 1, 0

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9. For l = 2, what are the possible values of ml?

1, 0, -1

1, 0

2, 1, 0

2, 1, 0, -1, -2

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10. Give the values for n, l, and ml for each orbital in the 2p subshell.

n = 2, l = 1, ml = 1, 0, -1

n = 2, l = 1, ml = 0

n = 2, l = 0, ml = 0

n = 2, l = 2, ml = 2, 1, 0, -1, -2

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11. Explain why the effective nuclear charge experienced by a 2p electron in fluorine is larger than that experienced by a 2p electron in boron.

The average number of electrons between a 2p electron

and the nucleus is greater in B than in F.

F has a larger nuclear charge than B.

They have different principal quantum numbers.

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12. For the hydrogen atom, which is highest in energy--the 2s, the 3s, or 2p orbital?

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13. Write the electron configuration for the atom Zn, using the appropriate noble-gas inner core for abbreviation.

[Ar]4s23d10

[Ar]4s24d10

[Kr]4s23d10

[Kr]4s24d10

[Ar]4s13d10

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14. Identify the specific element that corresponds to the following electron configuration: [Kr]5s24d105p4

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15. In which of the following sets are all of the ions or atoms isoelectronic with each other?

(i)K+, Na+, Mg2+

(ii)Ag+, Cd2+

(iii)Se2-, Te2-, Kr

(iv)Ru2+, Rh3+

(v)As3-, Se2-, Br-

iii

ii, iv, and v

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16. In which of the following sets are all of the ions or atoms isoelectronic with one another?

(i)Ba, Lu+, Hf3+

(ii)Nb4+, Y2+, Rb+1

(iii)Te2-, I-, Xe

(iv)Br-, Kr, Rb+

i only

ii only

iii only

iv only

i and ii only

iii and iv only

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17. Arrange the following atoms in order of increasing atomic radius: N, K, As, Fr

N < As < K < Fr

As < K < N < Fr

Fr < K < As < N

N < K < As < Fr

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18. Which of the following is the largest atom?

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19. Which of the following is correctly arranged with respect to the size of the atom/ion?

(i)Br+1 > Br > Br-

(ii)Rb+1 > K+1 > Na+1

(iii)Ru > Ru2+ > Ru3+

iii

i and iii

i and ii

ii and iii

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20. For the following set of atoms and ions, arrange the members in order of increasing size:

Te2-, Br, Rb+, Br-, Se2-

Te2- > Se2- > Br > Br- > Rb+

Te2- > Se2- > Br- > Br > Rb+

Se2- > Te2- > Br- > Br > Rb+

Te2- > Br- > Se2- > Br > Rb+

Te2- > Se2- > Br- > Rb+ > Br