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)

nlSubshellml values# Orbitals
101s01
202s01
12p-1, 0, +13
303s01
13p-1, 0, +13
23d-2, -1, 0, +1, +25
404s01
14p-1, 0, +13
24d-2, -1, 0, +1, +25
34f-3 to +37
$$\text{Quantum Numbers}$$
ElementElectronsConfiguration
Li31s2 2s1
Be41s2 2s2
B51s2 2s2 2p1
C61s2 2s2 2p2
N71s2 2s2 2p3
Ne101s2 2s2 2p6
Na111s2 2s2 2p6 3s1
$$\text{Electron Configurations (Light Elements)}$$
Group 2AGroup 3A
Be[He] 2s2B[He] 2s2 2p1
Mg[Ne] 3s2Al[Ne] 3s2 3p1
Ca[Ar] 4s2Ga[Ar] 3d10 4s2 4p1
Sr[Kr] 5s2In[Kr] 4d10 5s2 5p1
Ba[Xe] 6s2Tl[Xe] 4f14 5d10 6s2 6p1
$$\text{Group Electron Configurations}$$

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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