Bohrs Model of Hydrogen Atom - UNSOLVED PRACTICE SET
Chapter: Atoms | Topic: Bohrs Model of Hydrogen Atom
BOHRS MODEL OF HYDROGEN ATOM - UNSOLVED PRACTICE SET
Topic: Bohrs Model of Hydrogen Atom
Multiple Choice Questions
Q1. Bohr's model of the hydrogen atom is based on:
- Classical mechanics only
- Quantum theory only
- A combination of classical mechanics and quantum concepts
- Relativistic mechanics
Q2. According to Bohr's first postulate, electrons revolve in certain stable orbits called:
- Random orbits
- Stationary orbits
- Elliptical orbits only
- Hyperbolic orbits
Q3. Bohr's quantization condition for angular momentum is:
- L = nh
- L = nh/2ฯ
- L = nยฒh/2ฯ
- L = h/n
Q4. The radius of the nth orbit in a hydrogen atom is proportional to:
- n
- nยฒ
- 1/n
- 1/nยฒ
Q5. The speed of the electron in the nth orbit of a hydrogen atom is proportional to:
- n
- nยฒ
- 1/n
- 1/nยฒ
Q6. Bohr's model was successful in explaining:
- The spectrum of all atoms
- The spectrum of hydrogen and hydrogen-like atoms only
- The spectrum of multi-electron atoms
- The continuous spectrum of solids
Short Answer Questions
Q7. State the three postulates of Bohr's model of the hydrogen atom.
Q8. What is meant by a stationary orbit in Bohr's model? Why does the electron not radiate energy while moving in a stationary orbit?
Q9. Derive the expression for the radius of the first Bohr orbit (Bohr radius) in a hydrogen atom.
Q10. Why does Bohr's model fail to explain the spectrum of multi-electron atoms?
Q11. Calculate the speed of the electron in the first Bohr orbit of hydrogen.
Q12. What is the significance of the Bohr radius (aโ = 0.529 ร )?
Long Answer Questions
Q13. State the postulates of Bohr's model of the hydrogen atom. Derive the expression for the radius of the nth orbit and show that it is proportional to nยฒ.
Q14. Derive the expression for the total energy of the electron in the nth orbit of a hydrogen atom. Show that the energy is negative and inversely proportional to nยฒ.
Q15. Explain how Bohr's model successfully explains the stability of the hydrogen atom and the emission of line spectra. Why did this model fail for multi-electron atoms?
Numerical & Application-based Problems
Q16. For a hydrogen atom:
(a) Calculate the radius of the second Bohr orbit.
(b) Calculate the speed of the electron in the second orbit.
(c) Calculate the total energy of the electron in the second orbit.
(d) Calculate the angular momentum of the electron in the second orbit.
Q17. An electron in a hydrogen atom makes a transition from the n = 4 orbit to the n = 2 orbit.
(a) Calculate the energy of the electron in each orbit.
(b) Calculate the energy of the emitted photon.
(c) Calculate the wavelength of the emitted photon.
(d) Identify the spectral series to which this transition belongs.
Q18. In your school's physics lab, a student is studying Bohr's model using a computer simulation.
(a) She observes that the electron in the ground state of hydrogen has a total energy of โ13.6 eV. Calculate the kinetic energy and potential energy of the electron separately, and verify that their sum equals the total energy.
(b) The student then considers an electron in the n = 3 orbit. Calculate the number of revolutions the electron makes per second around the nucleus, and the time taken for one revolution.
(c) A classmate argues that since the electron is accelerating (moving in a circle), it should radiate energy and spiral into the nucleus according to classical physics. Explain how Bohr's postulates resolve this paradox.
(d) The student learns that the Bohr model gives the correct ionization energy of hydrogen (13.6 eV) but fails for helium. Explain why the model fails for helium and what additional complications arise in multi-electron atoms.
(e) In the context of modern physics, explain why Bohr's model is still taught in schools despite being superseded by quantum mechanics, and what important concepts from Bohr's model remain valid.