Atomic Structure — Practice Quiz

A Chemistry cheat sheet for Atomic Structure — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

Wave Equation: Speed of light equals wavelength times frequency.

$$c = \lambda \nu$$

Where: c = 3.00 × 10<sup>8</sup> m/s, λ = wavelength (m), ν = frequency (s<sup>-1</sup>)

Photon Energy: Energy of a photon.

$$E = h\nu$$

Where: h = Planck's constant (6.626 × 10<sup>-34</sup> J·s), ν = frequency (s<sup>-1</sup>)

de Broglie Wavelength: Matter as a wave.

$$\lambda = \frac{h}{mv}$$

Where: h = Planck's constant (6.626 × 10<sup>-34</sup> J·s), m = mass (kg), v = velocity (m/s)

Bohr Model Energy Levels: Energy of electron in hydrogen atom (Equation 6.4).

$$E_n = -\frac{2.18 \times 10^{-18} \text{ J}}{n^2}$$

Where: n = principal quantum number (1, 2, 3, ...)

Energy Change in Hydrogen: Energy change when electron transitions between levels (Equation 6.5).

$$\Delta E = E_{\text{final}} - E_{\text{initial}} = 2.18 \times 10^{-18} \text{ J} \left(\frac{1}{n_i^2} - \frac{1}{n_f^2}\right)$$

Where: n<sub>i</sub> = initial level, n<sub>f</sub> = final level

Heisenberg Uncertainty Principle: The uncertainty in position and momentum cannot both be zero.

$$\Delta x \times \Delta(mv) \geq \frac{h}{4\pi}$$

Where: Δx = uncertainty in position, Δ(mv) = uncertainty in momentum, h = Planck's constant

Effective Nuclear Charge: The net nuclear charge experienced by an electron (Equation 7.1).

$$Z_{\text{eff}} = Z - S$$

Where: Z = atomic number (number of protons), S = screening constant (number of core electrons)

<table style="width:100%; border-collapse: collapse; font-size: 0.85em;"> <tr style="border-bottom: 1px solid #ccc;"><th>n</th><th>l</th><th>Subshell</th><th>m<sub>l</sub> values</th><th># Orbitals</th></tr> <tr><td>1</td><td>0</td><td>1s</td><td>0</td><td>1</td></tr> <tr><td rowspan="2">2</td><td>0</td><td>2s</td><td>0</td><td>1</td></tr> <tr><td>1</td><td>2p</td><td>-1, 0, +1</td><td>3</td></tr> <tr><td rowspan="3">3</td><td>0</td><td>3s</td><td>0</td><td>1</td></tr> <tr><td>1</td><td>3p</td><td>-1, 0, +1</td><td>3</td></tr> <tr><td>2</td><td>3d</td><td>-2, -1, 0, +1, +2</td><td>5</td></tr> <tr><td rowspan="4">4</td><td>0</td><td>4s</td><td>0</td><td>1</td></tr> <tr><td>1</td><td>4p</td><td>-1, 0, +1</td><td>3</td></tr> <tr><td>2</td><td>4d</td><td>-2, -1, 0, +1, +2</td><td>5</td></tr> <tr><td>3</td><td>4f</td><td>-3 to +3</td><td>7</td></tr> </table>

$$\text{Quantum Numbers}$$

<table style="width:100%; border-collapse: collapse; font-size: 0.85em;"> <tr style="border-bottom: 1px solid #ccc;"><th>Element</th><th>Electrons</th><th>Configuration</th></tr> <tr><td>Li</td><td>3</td><td>1s<sup>2</sup> 2s<sup>1</sup></td></tr> <tr><td>Be</td><td>4</td><td>1s<sup>2</sup> 2s<sup>2</sup></td></tr> <tr><td>B</td><td>5</td><td>1s<sup>2</sup> 2s<sup>2</sup> 2p<sup>1</sup></td></tr> <tr><td>C</td><td>6</td><td>1s<sup>2</sup> 2s<sup>2</sup> 2p<sup>2</sup></td></tr> <tr><td>N</td><td>7</td><td>1s<sup>2</sup> 2s<sup>2</sup> 2p<sup>3</sup></td></tr> <tr><td>Ne</td><td>10</td><td>1s<sup>2</sup> 2s<sup>2</sup> 2p<sup>6</sup></td></tr> <tr><td>Na</td><td>11</td><td>1s<sup>2</sup> 2s<sup>2</sup> 2p<sup>6</sup> 3s<sup>1</sup></td></tr> </table>

$$\text{Electron Configurations (Light Elements)}$$

<table style="width:100%; border-collapse: collapse; font-size: 0.85em;"> <tr style="border-bottom: 1px solid #ccc;"><th colspan="2">Group 2A</th><th colspan="2">Group 3A</th></tr> <tr><td>Be</td><td>[He] 2s<sup>2</sup></td><td>B</td><td>[He] 2s<sup>2</sup> 2p<sup>1</sup></td></tr> <tr><td>Mg</td><td>[Ne] 3s<sup>2</sup></td><td>Al</td><td>[Ne] 3s<sup>2</sup> 3p<sup>1</sup></td></tr> <tr><td>Ca</td><td>[Ar] 4s<sup>2</sup></td><td>Ga</td><td>[Ar] 3d<sup>10</sup> 4s<sup>2</sup> 4p<sup>1</sup></td></tr> <tr><td>Sr</td><td>[Kr] 5s<sup>2</sup></td><td>In</td><td>[Kr] 4d<sup>10</sup> 5s<sup>2</sup> 5p<sup>1</sup></td></tr> <tr><td>Ba</td><td>[Xe] 6s<sup>2</sup></td><td>Tl</td><td>[Xe] 4f<sup>14</sup> 5d<sup>10</sup> 6s<sup>2</sup> 6p<sup>1</sup></td></tr> </table>

$$\text{Group Electron Configurations}$$

Practice quiz

  1. What is the frequency of a photon with a wavelength of $550 \text{ nm}$? (Given: speed of light $c = 3.00 \times 10^8 \text{ m/s}$)

    • $5.45 \times 10^{14} \text{ s}^{-1}$
    • $1.83 \times 10^{-15} \text{ s}^{-1}$
    • $5.45 \times 10^5 \text{ s}^{-1}$
    • $1.65 \times 10^{11} \text{ s}^{-1}$

    Answer: $5.45 \times 10^{14} \text{ s}^{-1}$

  2. What is the energy of a photon with a frequency of $7.50 \times 10^{14} \text{ Hz}$? (Given: Planck's constant $h = 6.626 \times 10^{-34} \text{ J} \cdot \text{s}$)

    • $4.97 \times 10^{-19} \text{ J}$
    • $1.13 \times 10^{-48} \text{ J}$
    • $2.21 \times 10^{-19} \text{ J}$
    • $4.97 \times 10^{-48} \text{ J}$

    Answer: $4.97 \times 10^{-19} \text{ J}$

  3. An electron with a mass of $9.109 \times 10^{-31} \text{ kg}$ is traveling at a velocity of $1.00 \times 10^6 \text{ m/s}$. What is its de Broglie wavelength? (Given: Planck's constant $h = 6.626 \times 10^{-34} \text{ J} \cdot \text{s}$)

    • $7.27 \times 10^{-10} \text{ m}$
    • $1.37 \times 10^9 \text{ m}$
    • $6.03 \times 10^{-7} \text{ m}$
    • $1.09 \times 10^{-12} \text{ m}$

    Answer: $7.27 \times 10^{-10} \text{ m}$

  4. According to the Bohr model, what is the energy of an electron in the $n=3$ energy level of a hydrogen atom? (Given: $E_n = -\frac{2.18 \times 10^{-18} \text{ J}}{n^2}$)

    • $-2.42 \times 10^{-19} \text{ J}$
    • $-2.18 \times 10^{-18} \text{ J}$
    • $-7.27 \times 10^{-19} \text{ J}$
    • $-4.84 \times 10^{-19} \text{ J}$

    Answer: $-2.42 \times 10^{-19} \text{ J}$

  5. What is the energy change when an electron in a hydrogen atom transitions from the $n_i=4$ state to the $n_f=2$ state? Is energy absorbed or emitted? (Given: $\Delta E = 2.18 \times 10^{-18} \text{ J} \left(\frac{1}{n_i^2} - \frac{1}{n_f^2}\right)$)

    • $-4.09 \times 10^{-19} \text{ J}$, emitted
    • $+4.09 \times 10^{-19} \text{ J}$, absorbed
    • $-1.63 \times 10^{-18} \text{ J}$, emitted
    • $+1.63 \times 10^{-18} \text{ J}$, absorbed

    Answer: $-4.09 \times 10^{-19} \text{ J}$, emitted

  6. Which of the following statements accurately describes the Heisenberg Uncertainty Principle?

    • It is impossible to simultaneously know with perfect accuracy both the position and momentum of a particle.
    • The energy of an electron in an atom is quantized and can only exist at specific energy levels.
    • Light exhibits properties of both waves and particles.
    • Electrons orbit the nucleus in fixed, circular paths.

    Answer: It is impossible to simultaneously know with perfect accuracy both the position and momentum of a particle.

  7. What is the effective nuclear charge ($Z_{\text{eff}}$) experienced by a valence electron in a neutral Sodium (Na) atom? (Atomic number $Z=11$)

    • $1$
    • $11$
    • $2$
    • $10$

    Answer: $1$

  8. Which of the following sets of quantum numbers ($n, l, m_l, m_s$) represents a valid state for an electron in an atom?

    • $n=3, l=3, m_l=0, m_s=+1/2$
    • $n=2, l=1, m_l=-2, m_s=-1/2$
    • $n=4, l=2, m_l=0, m_s=+1/2$
    • $n=1, l=1, m_l=0, m_s=-1/2$

    Answer: $n=4, l=2, m_l=0, m_s=+1/2$

  9. What is the correct ground state electron configuration for a neutral Nitrogen (N) atom? (Atomic number $Z=7$)

    • $1s^2 2s^2 2p^3$
    • $1s^2 2s^2 2p^2 3s^1$
    • $1s^2 2s^3 2p^2$
    • $1s^2 2s^2 2p^4$

    Answer: $1s^2 2s^2 2p^3$

  10. An element has the electron configuration $[Ar] 3d^{10} 4s^2 4p^1$. Based on this configuration, to which group in the periodic table does this element belong?

    • Group 2A
    • Group 3A
    • Group 4A
    • Group 1B

    Answer: Group 3A

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