Bohrs Model Postulates and Limitations - UNSOLVED PRACTICE SET

Q7. State any two postulates of Bohr's model of the hydrogen atom. 

Q8. What is the significance of the negative sign in the expression for the energy of an electron in a Bohr orbit? 

Q9. Define ground state and excited state of an electron in an atom. 

Q10. Why does an electron not lose energy while revolving in a stationary orbit according to Bohr?

Q11. Your school has a staircase with steps numbered 1, 2, 3, and so on. A student can stand on any step but not between steps. When the student jumps from step 3 to step 1, energy is released. How is this analogous to Bohr's model of electron transitions in an atom? What does each "step" represent? 

Q12. List any two limitations of Bohr's model.

Q13. State the postulates of Bohr's model of the hydrogen atom. Derive the expression for the radius of the nth orbit and the energy of the electron in the nth orbit. Explain why the energy is negative and what happens when n approaches infinity.

Q14. Explain how Bohr's model accounts for the line spectrum of hydrogen. Describe the different spectral series (Lyman, Balmer, Paschen) and the transitions responsible for each. Why could Bohr's model not explain the spectrum of atoms with more than one electron?

Q15. During a class discussion on atomic models, your teacher presents the following scenario:

(a) An electron in a hydrogen atom jumps from n = 4 to n = 2. In which spectral series does this transition lie? Is the emitted light visible?

(b) An electron absorbs energy and jumps from n = 1 to n = 3. How much energy must it absorb? What happens to this energy if the electron falls back to n = 1?

(c) Bohr's model works perfectly for hydrogen but fails for helium. Explain why, considering that helium has two electrons.

(d) Despite its limitations, why is Bohr's model still taught in schools? What important concepts does it introduce that remain relevant in quantum mechanics?

Q16. For a hydrogen atom, the energy of the electron in the nth orbit is given by Eₙ = −13.6/n² eV.

(a) Calculate the energy of the electron in the first orbit (n = 1).

(b) Calculate the energy required to excite an electron from n = 1 to n = 3.

(c) Calculate the wavelength of light emitted when an electron falls from n = 3 to n = 2.

(1 eV = 1.6 × 10⁻¹⁹ J, h = 6.626 × 10⁻³⁴ J·s, c = 3 × 10⁸ m/s)

Q17. The radius of the nth Bohr orbit is given by rₙ = 0.529 × n² Å.

(a) Calculate the radius of the first, second, and third Bohr orbits.

(b) Calculate the ratio of the radii of the 2nd orbit to the 1st orbit, and the 3rd orbit to the 2nd orbit.

(c) If an electron moves from the 3rd orbit to the 2nd orbit, calculate the change in orbital radius.

(d) Why does the radius increase as n² and not linearly with n?

Q18. The Rydberg constant for hydrogen is 1.097 × 10⁷ m⁻¹. The wavelength of spectral lines is given by 1/λ = R(1/n₁² − 1/n₂²).

(a) Calculate the wavelength of the first line of the Lyman series (n₁ = 1, n₂ = 2).

(b) Calculate the wavelength of the first line of the Balmer series (n₁ = 2, n₂ = 3).

(c) Which of these lines lies in the visible region? Explain.

(d) Calculate the shortest wavelength in the Balmer series (n₂ = ∞).

(c = 3 × 10⁸ m/s)