AP Physics 2 Flashcards: The Bohr Model Of Atomic Structure

What this deck covers

This deck focuses on The Bohr Model Of Atomic Structure, giving you a quick way to review the definitions, rules, and examples that matter most for AP Physics 2.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is $a_0$ in the Bohr Model formula for orbit radius?

Answer: The Bohr radius, approximately $5.29 \times 10^{-11}$ m. The radius of the first electron orbit in hydrogen.

Flashcard 2: What is the energy of the electron in the ground state according to the Bohr Model?

Answer: $-13.6$ eV. This is the ionization energy of hydrogen with opposite sign.

Flashcard 3: What is the speed of an electron in the first Bohr orbit?

Answer: Approximately $2.18 \times 10^6$ m/s. Calculated from $v_1 = \frac{ke^2}{\text{ħ}}$ for $n=1$.

Flashcard 4: Identify a key difference between classical and Bohr Model of the atom.

Answer: Bohr Model includes quantized orbits. Classical physics predicted continuous energy and orbital decay.

Flashcard 5: Calculate the energy change for $n=4$ to $n=2$ transition in hydrogen.

Answer: $2.55$ eV. Energy difference: $E_4 - E_2 = -0.85 - (-3.4) = 2.55$ eV.

Flashcard 6: What physical concept is central to the Bohr Model's explanation of atomic spectra?

Answer: Quantization. Energy and angular momentum can only have discrete values.

Flashcard 7: Identify the series of spectral lines resulting from electron transitions to $n=1$.

Answer: Lyman series. UV region transitions from higher levels to ground state.

Flashcard 8: What is the primary postulate of the Bohr Model?

Answer: Electrons orbit the nucleus in fixed energy levels. This quantization prevents classical electromagnetic radiation losses.

Flashcard 9: Which element did Niels Bohr primarily study when developing his model?

Answer: Hydrogen. Its simple one-electron structure made calculations feasible.

Flashcard 10: What series describes transitions to $n=2$ in the hydrogen atom?

Answer: Balmer series. Visible region transitions producing the familiar hydrogen spectrum.

Flashcard 11: What is the condition for stable electron orbits in the Bohr Model?

Answer: Angular momentum is quantized. Only integer multiples of $\frac{h}{2\pi}$ are allowed.

Flashcard 12: What is the formula for the speed of an electron in the Bohr Model?

Answer: $v_n = \frac{k e^2}{\text{ħ} n}$. Where $e$ is electron charge and $\text{ħ}$ is reduced Planck's constant.

Flashcard 13: State the formula for the energy of an electron in the Bohr Model.

Answer: $E_n = -\frac{13.6 \text{ eV}}{n^2}$. Energy decreases as $n^2$ increases, with ground state at $n=1$.

Flashcard 14: Which transition emits the longest wavelength in the hydrogen spectrum?

Answer: $n=3$ to $n=2$ transition. Smallest energy difference produces longest wavelength photon.

Flashcard 15: Identify the series describing transitions to $n=3$ in hydrogen.

Answer: Paschen series. Infrared region transitions from higher levels to $n=3$.

Flashcard 16: Calculate the radius of the first Bohr orbit for hydrogen.

Answer: $5.29 \times 10^{-11}$ m. Using $r_1 = 1^2 \times a_0$ where $a_0 = 5.29 \times 10^{-11}$ m.

Flashcard 17: What aspect of atoms does the Bohr Model fail to explain?

Answer: Fine structure and Zeeman effect. These require relativistic effects and spin considerations.

Flashcard 18: Identify the series describing transitions to $n=3$ in hydrogen.

Answer: Paschen series. Infrared region transitions from higher levels to $n=3$.

Flashcard 19: How is the frequency of emitted radiation calculated in the Bohr Model?

Answer: $f = \frac{E_i - E_f}{h}$. Energy difference between levels divided by Planck's constant.

Flashcard 20: What is the main limitation of the Bohr Model?

Answer: It only accurately describes hydrogen-like atoms. Multi-electron atoms involve complex electron-electron interactions.

Flashcard 21: Identify the constant $h$ in the frequency formula of the Bohr Model.

Answer: Planck's constant. Fundamental constant linking energy and frequency: $6.626 \times 10^{-34}$ J·s.

Flashcard 22: Define the term 'quantum leap' as used in the Bohr Model.

Answer: An electron transition between energy levels. Electrons jump instantly between allowed energy states.

Flashcard 23: What is the formula for the speed of an electron in the Bohr Model?

Answer: $v_n = \frac{k e^2}{\hbar n}$. Where $e$ is electron charge and $\hbar$ is reduced Planck's constant.

Flashcard 24: What is the primary postulate of the Bohr Model?

Answer: Electrons orbit the nucleus in fixed energy levels. This quantization prevents classical electromagnetic radiation losses.

Flashcard 25: What experimental evidence supports the Bohr Model?

Answer: Hydrogen emission spectrum. Discrete spectral lines match calculated energy differences.

Flashcard 26: What is the relationship between orbit radius and energy level in the Bohr Model?

Answer: Radius increases as $n^2$. Higher energy levels correspond to larger orbital radii.

Flashcard 27: How does the Bohr Model account for the stability of electron orbits?

Answer: Quantized energy levels prevent spiraling into nucleus. Only specific orbits are allowed, preventing energy loss.

Flashcard 28: Identify a key difference between classical and Bohr Model of the atom.

Answer: Bohr Model includes quantized orbits. Classical physics predicted continuous energy and orbital decay.

Flashcard 29: What is the formula for the wavelength of emitted radiation in the Bohr Model?

Answer: $\frac{1}{\lambda} = R_H \times (\frac{1}{n_1^2} - \frac{1}{n_2^2})$. Rydberg formula relating wavelength to quantum number transitions.

Flashcard 30: What is the main limitation of the Bohr Model?

Answer: It only accurately describes hydrogen-like atoms. Multi-electron atoms involve complex electron-electron interactions.

Flashcard 31: Describe the significance of the Rydberg constant in the Bohr Model.

Answer: Used to calculate wavelengths of spectral lines. Essential for predicting hydrogen's emission and absorption spectra.

Flashcard 32: State the formula for the radius of an electron orbit in the Bohr Model.

Answer: $r_n = n^2 \times a_0$. Where $n$ is the principal quantum number and $a_0$ is the Bohr radius.

Flashcard 33: Calculate the radius of the first Bohr orbit for hydrogen.

Answer: $5.29 \times 10^{-11}$ m. Using $r_1 = 1^2 \times a_0$ where $a_0 = 5.29 \times 10^{-11}$ m.

Flashcard 34: What does $R_H$ represent in the wavelength formula?

Answer: Rydberg constant. Empirical constant: $1.097 \times 10^7$ m⁻¹ for hydrogen.

Flashcard 35: Calculate the frequency of the photon emitted during $n=3$ to $n=2$ transition.

Answer: Approximately $4.57 \times 10^{14}$ Hz. Using $f = \frac{E_3 - E_2}{h} = \frac{1.89 \text{ eV}}{h}$.

Flashcard 36: How does the Bohr Model explain the emission spectrum of hydrogen?

Answer: Transitions between energy levels. Each line corresponds to a specific energy level change.

Flashcard 37: How is the frequency of emitted radiation calculated in the Bohr Model?

Answer: $f = \frac{E_i - E_f}{h}$. Energy difference between levels divided by Planck's constant.

Flashcard 38: What does $k$ represent in the speed formula of the Bohr Model?

Answer: Coulomb's constant. Electrostatic force constant: $8.99 \times 10^9$ N·m²/C².

Flashcard 39: Identify the constant $h$ in the frequency formula of the Bohr Model.

Answer: Planck's constant. Fundamental constant linking energy and frequency: $6.626 \times 10^{-34}$ J·s.

Flashcard 40: What is the significance of quantized energy levels in the Bohr Model?

Answer: Electrons have fixed energies corresponding to orbits. No intermediate energies are allowed between levels.

Flashcard 41: What is $a_0$ in the Bohr Model formula for orbit radius?

Answer: The Bohr radius, approximately $5.29 \times 10^{-11}$ m. The radius of the first electron orbit in hydrogen.

Flashcard 42: Which physical constant is central to the Bohr Model calculations?

Answer: Planck's constant, $h$. It appears in energy quantization and angular momentum conditions.

Flashcard 43: State the angular momentum quantization condition in the Bohr Model.

Answer: $L = n \times \frac{h}{2\text{π}}$. Where $\text{ħ} = \frac{h}{2\text{π}}$ is reduced Planck's constant.

Flashcard 44: What is the main assumption about electron movement in the Bohr Model?

Answer: Electrons move in circular orbits. Classical planetary model with quantization constraints.

Flashcard 45: What physical concept is central to the Bohr Model's explanation of atomic spectra?

Answer: Quantization. Energy and angular momentum can only have discrete values.

Flashcard 46: What series describes transitions to $n=2$ in the hydrogen atom?

Answer: Balmer series. Visible region transitions producing the familiar hydrogen spectrum.

Flashcard 47: What is the primary reason for the success of the Bohr Model?

Answer: Accurate prediction of hydrogen spectral lines. Quantized energy levels perfectly matched observed spectral lines.

Flashcard 48: What is the condition for stable electron orbits in the Bohr Model?

Answer: Angular momentum is quantized. Only integer multiples of $\frac{h}{2\text{π}}$ are allowed.

Flashcard 49: What does $R_H$ represent in the wavelength formula?

Answer: Rydberg constant. Empirical constant: $1.097 \times 10^7$ m⁻¹ for hydrogen.

Flashcard 50: What is the relationship between orbit radius and energy level in the Bohr Model?

Answer: Radius increases as $n^2$. Higher energy levels correspond to larger orbital radii.

Flashcard 51: Which element did Niels Bohr primarily study when developing his model?

Answer: Hydrogen. Its simple one-electron structure made calculations feasible.

Flashcard 52: Define the term 'quantum leap' as used in the Bohr Model.

Answer: An electron transition between energy levels. Electrons jump instantly between allowed energy states.

Flashcard 53: Which physical constant is central to the Bohr Model calculations?

Answer: Planck's constant, $h$. It appears in energy quantization and angular momentum conditions.

Flashcard 54: What is the formula for the wavelength of emitted radiation in the Bohr Model?

Answer: $\frac{1}{\text{λ}} = R_H \times (\frac{1}{n_1^2} - \frac{1}{n_2^2})$. Rydberg formula relating wavelength to quantum number transitions.

Flashcard 55: Describe the significance of the Rydberg constant in the Bohr Model.

Answer: Used to calculate wavelengths of spectral lines. Essential for predicting hydrogen's emission and absorption spectra.

Flashcard 56: What experimental evidence supports the Bohr Model?

Answer: Hydrogen emission spectrum. Discrete spectral lines match calculated energy differences.

Flashcard 57: What does $n$ represent in the Bohr Model?

Answer: The principal quantum number. It determines the energy level and orbit radius of the electron.

Flashcard 58: What is the energy of the electron in the ground state according to the Bohr Model?

Answer: $-13.6$ eV. This is the ionization energy of hydrogen with opposite sign.

Flashcard 59: Calculate the energy change for $n=4$ to $n=2$ transition in hydrogen.

Answer: $2.55$ eV. Energy difference: $E_4 - E_2 = -0.85 - (-3.4) = 2.55$ eV.

Flashcard 60: What does $k$ represent in the speed formula of the Bohr Model?

Answer: Coulomb's constant. Electrostatic force constant: $8.99 \times 10^9$ N·m²/C².

Flashcard 61: What is the main assumption about electron movement in the Bohr Model?

Answer: Electrons move in circular orbits. Classical planetary model with quantization constraints.

Flashcard 62: What is the primary reason for the success of the Bohr Model?

Answer: Accurate prediction of hydrogen spectral lines. Quantized energy levels perfectly matched observed spectral lines.

Flashcard 63: State the formula for the radius of an electron orbit in the Bohr Model.

Answer: $r_n = n^2 \times a_0$. Where $n$ is the principal quantum number and $a_0$ is the Bohr radius.

Flashcard 64: What is the speed of an electron in the first Bohr orbit?

Answer: Approximately $2.18 \times 10^6$ m/s. Calculated from $v_1 = \frac{ke^2}{\text{ħ}}$ for $n=1$.

Flashcard 65: Identify the series of spectral lines resulting from electron transitions to $n=1$.

Answer: Lyman series. UV region transitions from higher levels to ground state.

Flashcard 66: What is the significance of quantized energy levels in the Bohr Model?

Answer: Electrons have fixed energies corresponding to orbits. No intermediate energies are allowed between levels.

Flashcard 67: Calculate the wavelength for $n=4$ to $n=2$ transition in hydrogen.

Answer: Approximately $486$ nm. Using Rydberg formula with $n_1=2$, $n_2=4$.

Flashcard 68: Which transition emits the longest wavelength in the hydrogen spectrum?

Answer: $n=3$ to $n=2$ transition. Smallest energy difference produces longest wavelength photon.

Flashcard 69: Calculate the energy of an electron in the second energy level of hydrogen.

Answer: $-3.4$ eV. Using $E_2 = -\frac{13.6}{2^2} = -3.4$ eV.

Flashcard 70: Calculate the energy of an electron in the second energy level of hydrogen.

Answer: $-3.4$ eV. Using $E_2 = -\frac{13.6}{2^2} = -3.4$ eV.

Flashcard 71: What aspect of atoms does the Bohr Model fail to explain?

Answer: Fine structure and Zeeman effect. These require relativistic effects and spin considerations.

Flashcard 72: Calculate the wavelength for $n=4$ to $n=2$ transition in hydrogen.

Answer: Approximately $486$ nm. Using Rydberg formula with $n_1=2$, $n_2=4$.

Flashcard 73: How does the Bohr Model account for the stability of electron orbits?

Answer: Quantized energy levels prevent spiraling into nucleus. Only specific orbits are allowed, preventing energy loss.

Flashcard 74: State the angular momentum quantization condition in the Bohr Model.

Answer: $L = n \times \frac{h}{2\text{π}}$. Where $\text{ħ} = \frac{h}{2\text{π}}$ is reduced Planck's constant.

Flashcard 75: What does $n$ represent in the Bohr Model?

Answer: The principal quantum number. It determines the energy level and orbit radius of the electron.

Flashcard 76: State the formula for the energy of an electron in the Bohr Model.

Answer: $E_n = -\frac{13.6 \text{ eV}}{n^2}$. Energy decreases as $n^2$ increases, with ground state at $n=1$.

Flashcard 77: Calculate the frequency of the photon emitted during $n=3$ to $n=2$ transition.

Answer: Approximately $4.57 \times 10^{14}$ Hz. Using $f = \frac{E_3 - E_2}{h} = \frac{1.89 \text{ eV}}{h}$.

Flashcard 78: How does the Bohr Model explain the emission spectrum of hydrogen?

Answer: Transitions between energy levels. Each line corresponds to a specific energy level change.