The Bohr Model of Atomic Structure - AP Physics 2

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

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

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

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

3. Identify a key difference between classical and Bohr Model of the atom.

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

4. What is the primary postulate of the Bohr Model?

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

5. What series describes transitions to $n=2$ in the hydrogen atom?

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

6. What is the formula for the speed of an electron in the Bohr Model?

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

7. State the formula for the energy of an electron in the Bohr Model.

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

8. Which transition emits the longest wavelength in the hydrogen spectrum?

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

9. What aspect of atoms does the Bohr Model fail to explain?

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

10. Identify the series describing transitions to $n=3$ in hydrogen.

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

11. How is the frequency of emitted radiation calculated in the Bohr Model?

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

12. What experimental evidence supports the Bohr Model?

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

13. What is the relationship between orbit radius and energy level in the Bohr Model?

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

14. What is the main limitation of the Bohr Model?

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

15. Describe the significance of the Rydberg constant in the Bohr Model.

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

16. State the formula for the radius of an electron orbit in the Bohr Model.

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

17. Calculate the radius of the first Bohr orbit for hydrogen.

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

18. What does $R_H$ represent in the wavelength formula?

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

19. What does $k$ represent in the speed formula of the Bohr Model?

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

20. Identify the constant $h$ in the frequency formula of the Bohr Model.

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

21. What is the significance of quantized energy levels in the Bohr Model?

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

22. Which physical constant is central to the Bohr Model calculations?

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

23. What is the main assumption about electron movement in the Bohr Model?

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

24. What physical concept is central to the Bohr Model's explanation of atomic spectra?

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

25. What is the primary reason for the success of the Bohr Model?

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

26. What is the condition for stable electron orbits in the Bohr Model?

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

27. Which element did Niels Bohr primarily study when developing his model?

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

28. Define the term 'quantum leap' as used in the Bohr Model.

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

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

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

30. Calculate the energy change for $n=4$ to $n=2$ transition in hydrogen.

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

31. What is the speed of an electron in the first Bohr orbit?

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

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

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

33. Calculate the wavelength for $n=4$ to $n=2$ transition in hydrogen.

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

34. Calculate the energy of an electron in the second energy level of hydrogen.

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

35. How does the Bohr Model account for the stability of electron orbits?

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

36. State the angular momentum quantization condition in the Bohr Model.

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

37. What does $n$ represent in the Bohr Model?

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

38. Calculate the frequency of the photon emitted during $n=3$ to $n=2$ transition.

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

39. How does the Bohr Model explain the emission spectrum of hydrogen?

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

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