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6: The Structure of Atoms

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    Speed of Light

    Exercise \(\PageIndex{1}\)

    A device emits light at 512.8 nm.  What is the frequency of this radiation?

    Answer

    5.851 x 1014 Hz

    \[v = \frac{c}{\lambda }\]

    \[v\;=\;(\frac{2.99\;*\;10^{8}\;ms^{-1} }{512.8\;*\;10^{-9}})\]

    \[v\; = 5.8307\;*\;10^{14}\;Hz\]

    Exercise \(\PageIndex{2}\)

    What is the wavelength of a photon having a frequency of 75.9 THz?  (1 THz = 1015 Hz)

    Answer

    3.94 nm

    Exercise \(\PageIndex{3}\)

    What is the frequency of gamma ray radiation that has a wavelength of 15.6 pm?

    Answer

    1.92 × 1019 s–1

    Exercise \(\PageIndex{4}\)

    If a cordless phone operates at a frequency of 6.23 × 108 s–1, what is the wavelength of this radiation?

    Answer

    0.480 m

    Exercise \(\PageIndex{5}\)

    A device operates at a frequency of  1.25 x 1014 Hz.  What is the wavelength of this radiation?

    Answer

    0.239 nm

     

    Radiation and Planck's Constant

    Exercise \(\PageIndex{1}\)

    What is the energy of a photon of electromagnetic radiation with a wavelength of 256.8 nm? 

    Answer

    7.714 x 10-19 J

    \[E=\frac{h*c}{\lambda }\]

    \[E=\frac{(6.625*10^{-34}\;J*s)*(2.99*10^{8}\;m/s)}{(256.8*10^{-9}\;m)}=7.7136*10^{-19}\;J\]

    Exercise \(\PageIndex{2}\)

    What is the wavelength of a photon that has an energy of 3.861 x 104 J

    Answer

    5.130 x 10-21 nm

    Exercise \(\PageIndex{3}\)

    What is the energy of a photon of electromagnetic radiation with a frequency of 9.48 x 1014 Hz?

    Answer

    6.28 x 10-19 J

     

    Per Photon or Per Mole

    Exercise \(\PageIndex{4}\)

    A red laser pointer emits light at a wavelength of 580.9 nm. If the laser emits 1.84 × 10–4 J of energy per second in the form of visible radiation, how many photons per second are emitted from the laser?

    Answer

    5.40 × 1014 photons/sec

    \[E=\frac{hc}{\lambda }\]

    \[E=\frac{(6.625*10^{-34}\;J/s)(2.99*10^{8}\;m/s)}{(580.9*10^{-9})\;m}=5.395*10^{14}\;photons/sec\]

    Exercise \(\PageIndex{5}\)

    What is the energy per mole of photons of light with a wavelength of 690.8 nm?

    Answer

    8.210 × 102  kJ/mol

    \[E_{per\;mole}=\frac{N_{a}hc}{\lambda }\]

    \[E_{per\;mole}=\frac{(6.022*10^{23})(6.625*10^{-34})(2.99*0^{8})}{145.3*10^{-9}}=820979\;J/mol\]

    Exercise \(\PageIndex{6}\)

    What is the energy per mole of photons of light with a frequency of 2.98 × 1015  Hz?

    Answer

    1.19 × 103 kJ/mol

    Exercise \(\PageIndex{7}\)

    If the energy of 1.00 mole of photons is 658 kJ, what is the wavelength of the light?

    Answer

    181 nm

    Exercise \(\PageIndex{8}\)

    A light emitting diode (L.E.D.) emits photons with an energy of 6.359 x 10-19 J. What is the energy per mole of photons emitted? ​

    Answer

    3.829 x 105 J/mol

    Exercise \(\PageIndex{9}\)

    What is the binding energy of an electron in a photosensitive metal (in kJ/mol) if the longest wavelength of light that can eject electrons from the metal is 459.0 nm?

    Answer

    259.9 kJ/mol

    Exercise \(\PageIndex{10}\)

    The energy required to break one mole of fluorine-fluorine bonds in F2 is 155 kJ/mol. What is the longest wavelength of light capable of breaking a single F-F bond?

    Answer

    770 nm

     

    Rydberg Equation

    Exercise \(\PageIndex{1}\)

    What is the wavelength of light emitted when an electron in a hydrogen atom undergoes a transition from energy level n = 3 to level n = 1? (c  = 3.00  × 108 m/s, h =  6.63 × 10–34 J·s, RH  =  2.179 × 10–18 J)

    Answer

    102 nm

    \[\frac{hc}{\lambda } = R_{H}\left [(\frac{1}{(n_{1})^{2}})-(\frac{1}{(n_{2})^{2}}) \right ]\]

    \[\frac{(6.63*10^{-34})(3.00*10^{8})}{\lambda }=(2.179*10^{-18})(\frac{1}{1}-\frac{1}{9})\]
    \[\lambda = \frac{1.981*10^{-25}}{1.937*10^{-18}}\]

    \[\lambda = 1.023*10^{-7}\;m\] 

    Exercise \(\PageIndex{2}\)

    The electron in a hydrogen atom, originally in level n = 5, undergoes a transition to a lower level by emitting a photon of wavelength 1583 nm. What is the final level of the electron?  (c  = 3.00  × 108 m/s, h =  6.626 × 10–34 J·s, RH  =  2.179 × 10–18 J)

    Answer

    3

     

    Emission Lines 

    Exercise \(\PageIndex{3}\)

    If a hydrogen atom in the excited n = 5 state relaxes to the ground state, what is the maximum number of possible emission lines?

    Answer

    15

     

    de Broglie Wavelength

    Exercise \(\PageIndex{1}\)

    For a proton (mass = 1.673 × 10–27 kg) moving with a velocity of 8.63 × 104 m/s, what is the de Broglie wavelength of the proton (in pm)?

    Answer

    4.59 pm

    \[E = \frac{1}{2}mv^{2}\]

    \[E = \frac{1}{2}(1.673*10^{-27})(8.63*10^{4})^{2} = 6.229*10^{-18}\;J\]

    \[\lambda = \frac{h}{\sqrt{2Em}}\]

    \[\lambda = \frac{6.626*10^{-34}}{\sqrt{2*(6.229*10^{-18})*(1.673*10^{-27})}}\]
    \[\lambda = 4.588*10^{-12}\;m=4.588\;pm\]

    Exercise \(\PageIndex{1}\)

    What is the de Broglie wavelength of an electron traveling at 15.9% of the speed of light?  (c  = 3.00  × 108 m/s, h =  6.63 × 10–34 J·s, me  =  9.109 × 10–31 J)

    Answer

    1.52 × 10–11 m

    Exercise \(\PageIndex{1}\)

    If the de Broglie wavelength of an electron is 90.2 nm, what is its velocity? (The mass of an electron is 9.11 × 10–31 kg.)

    Answer

    8.06 × 103 m/s

    Exercise \(\PageIndex{1}\)

    What is the de Broglie wavelength of a 250-g baseball traveling at 85 mph?  (1 mi = 1.609 km and h =  6.63 × 10–34 J·s)

    Answer

    7.0 × 10-35 m

     

    Quantum Numbers

    Exercise \(\PageIndex{1}\)

    What is the value of the orbital angular momentum quantum number (l) for an electron in a 4f orbital?

    a. 1    b. 4    c. 2    d. 3    e. 0

    Answer

    d. 3

    Exercise \(\PageIndex{2}\)

    How many orbitals have the following set of quantum numbers: n = 5, l= 3, ml= –1?

    a. 0    b. 1    c. 3    d. 6    e. 7

    Answer

    b. 1 orbital

    Exercise \(\PageIndex{3}\)

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

    1. n = 4, l = 2, ml = -2
    2. n = 6, l = 1, ml = 1
    3. n = 5, l = 4, ml = -4
    4. n = 2, l = 1, ml = -3
    5. n = 6, l = 3, ml = -2
    Answer

    d. n = 2, l = 1, ml = -3

    Exercise \(\PageIndex{4}\)

    What is the total number of orbitals having n = 3 and l= 2?

    1. 1 orbital
    2. 3 orbitals
    3. 5 orbitals
    4. 7 orbitals
    5. 10 orbitals
    Answer

    a. 1 orbital

    Exercise \(\PageIndex{5}\)

    How many f orbitals are in the n = 4 shell?

    1. 5 f orbitals
    2. 8 f orbitals
    3. 3 f orbitals
    4. 1 f orbital
    5. 7 f orbitals
    Answer

    e. 7 f orbitals

    Exercise \(\PageIndex{6}\)

    What type of orbital is designated n = 4, l= 2, ml= 2?

    a. 4f    b. 4d    c. 4p    d. 4g    e. 4s

    Answer

    b. 4d

    Exercise \(\PageIndex{7}\)

    Which type of orbital is designated n = 2 and l= 1?

    a. 2p    b. 3s    c. 4d    d. 1f    e. 2d

    Answer

    a. 2p

    Exercise \(\PageIndex{8}\)

    Which of the following orbital can be represented by n = 4, l= 3, and ml = –2?

    a. 4s    b. 4p    c. 4d    d. 4f    e. None of these

    Answer

    d. 4f

    Exercise \(\PageIndex{9}\)

    A possible value of the magnetic quantum number ml for a 5p electron is

    a. 1    b. 4    c. 5    d. -6    e. 3

    Answer

    a. 1

    Exercise \(\PageIndex{10}\)

    How many values are there for the magnetic quantum number (ml) when the value of the angular momentum quantum number (l) is 4?

    a. 11    b. 9    c. 2    d. 4    e. 15

    Answer

    b. 9

    Exercise \(\PageIndex{11}\)

    What is the total number of subshells found in the n = 7 shell?

    a. 7    b. 49    c. 6    d. 8    e. 9

    Answer

    a. 7 subshells

    Exercise \(\PageIndex{12}\)

    Which of the following sets of quantum numbers refers to a 4d orbital?

    1. n = 2, l = 1, ml = -1
    2. n = 2, l = 4, ml = -1
    3. n = 4, l = 2, ml = -1
    4. n = 4, l = 3, ml = 0
    5. n = 4, l = 3, ml = +2
    Answer

    c. n = 4, l = 2, ml = -1

    Exercise \(\PageIndex{13}\)

    The (principal quantum number) n = ____ shell is the lowest that may contain s-orbitals.

    a. 1    b. 2    c. 3    d. 4    e. 5

    Answer

    a. 1

     

    Orbitals

    Exercise \(\PageIndex{1}\)

    A 4d orbital has ?

    1. 3 planar nodes and 3 spherical nodes
    2. 1 planar node and 1 spherical nodes
    3. 2 planar nodes and 1 spherical node
    4. 2 planar nodes and 4 spherical nodes
    5. 4 planar nodes and 2 spherical nodes
    Answer

    c. 2 planar nodes and 1 spherical node

    Exercise \(\PageIndex{2}\)

    Which of the following is a representation of a 3dxy orbital?

    1. clipboard_e00a9ff0b43917cae16e4a6ea7f7aec44.png
    2. clipboard_e6f8e63217f5d4a39794b4aa1b4857f6b.png
    3. clipboard_e65b5a005a23ffd142389374c6d5d3e48.png
    4. clipboard_ecca3c7101ad4c0b9cca7bdc5d4b25825.png
    5. clipboard_e5abe0734beec5b28cd23007c75b9fdac.png
    Answer

    a. clipboard_e00a9ff0b43917cae16e4a6ea7f7aec44.png

    Exercise \(\PageIndex{3}\)

    Which of the following orbital boundary surfaces represent d-orbitals?

    clipboard_e80a9f1d2938f102cab51692e9ef82b45.png

    a. 1 only        b. 3 only         c. 2 only         d. 1 and 2         e. 1 and 4

    Answer

    e. 1 and 4

    Exercise \(\PageIndex{4}\)

    Which of the following orbital boundary surfaces is a representation of a 3dz2 orbital?

    1. clipboard_e9ecf3f5584cc5e023ff302dab50f892b.png
    2. clipboard_efc978fca485736dfb5c20b418b2c4d69.png
    3. clipboard_ef76e40a9608dab43e8dcdc9e265dcc91.png
    4. clipboard_e396af069dbaeb4b3d2f9f20931521e2d.png
    5. clipboard_e3e27fc2cd98c4391553956fe5b3a5eb8.png
    Answer

    a. clipboard_e9ecf3f5584cc5e023ff302dab50f892b.png 

     

    Paramagnetic, Diamagnetic and Ferromagnetic

    Exercise \(\PageIndex{1}\)

    Which of the following statements is/are CORRECT?

    1. A paramagnetic substance is attracted to a magnetic field.
    2. An atom with no unpaired electrons is ferromagnetic.
    3. Atoms with one or more unpaired electrons are paramagnetic.

    a. 1 only         b. 3 only         c. 3 only         d. 1 and 3         e. 1,2, and 3

    Answer

    d. 1 and 3  

    Exercise \(\PageIndex{2}\)

    Which of the following statements is/are CORRECT?

    1. A diamagnetic substance is strongly attracted to a magnetic field.
    2. Substances that retain their magnetism after they are withdrawn from a magnetic field are called ferromagnetic.
    3. Most transition metals and all lanthanide metals are ferromagnetic.

    a. 1 only        b. 2 only        c. 3 only        d. 1 and 3        e. 1,2, and 3

    Answer

    b. 2 only

     

    Quantum Numbers and Spin

    Exercise \(\PageIndex{3}\)

    What is the value of the spin quantum number for an electron in a 3d orbital?

    1. 3
    2. 2
    3. either \(+\frac{1}{2}\) or \(-\frac{1}{2}\)
    4. \(-\frac{1}{2}\)
    5. \(+\frac{1}{2}\)
    Answer

    c. either \(+\frac{1}{2}\) or \(-\frac{1}{2}\)

    Exercise \(\PageIndex{4}\)

    Which of the following sets of quantum numbers (n, l, ml, ms) is not permissible?

    1. 2,  2,  1, \(+\frac{1}{2}\)
    2. 3,  1,  0,  \(-\frac{1}{2}\)
    3. 1, 0, 0, \(+\frac{1}{2}\)
    4. 2,  1,  0,  \(+\frac{1}{2}\)
    5. 4, 0,  0, \(-\frac{1}{2}\)
    Answer

    a. 2,  2,  1, \(+\frac{1}{2}\)

    6: The Structure of Atoms is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.

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