Bohr's Model + Hydrogen Spectrum
Atoms
58
JEE Qs
15%
Hard
75
min
Master the proportionality relations of radius, velocity, and energy with 'n' and 'Z' to quickly solve comparative questions for H-like species.
🧮 Key Formulas
✅ Key Points for JEE
- 1Bohr's model is valid only for single-electron species (H, He+, Li2+, etc.). Quantities like r, v, E scale as Z and n change: r ~ n^2/Z, v ~ Z/n, E ~ Z^2/n^2.
- 2The total energy (E) is always negative, signifying a bound state. Kinetic energy (K) = -E, and Potential energy (U) = 2E. Understand these relationships for problem-solving.
- 3Emission occurs when an electron transitions from a higher energy level (n_2) to a lower energy level (n_1), releasing a photon. Absorption occurs for the reverse transition.
- 4Memorize the spectral series: Lyman (n_1=1, UV), Balmer (n_1=2, Visible), Paschen (n_1=3, IR), Brackett (n_1=4, IR), Pfund (n_1=5, IR). The series limit corresponds to n_2 = ∞, giving minimum wavelength/maximum energy.
- 5Excitation energy is the energy required to promote an electron from a lower state to a higher state (E_final - E_initial). Ionization energy is the energy required to remove an electron completely from an atom (E_∞ - E_initial).
⚠️ Common Mistakes
- ✕Sign errors when calculating total, kinetic, and potential energies, or confusing their interrelationships.
- ✕Incorrectly applying the Rydberg formula, especially confusing n_1 and n_2, or forgetting the Z^2 factor for H-like atoms.
- ✕Not understanding that Bohr's model is limited to single-electron species and trying to apply it to multi-electron atoms.
- ✕Confusing the series limit (n_2=∞) with the longest wavelength (n_2=n_1+1) for a given series.
📝 Practice Questions
See allQ61.Given below are two statements about X-ray spectra of elements : Statement (I) : A plot of √v ( v = frequency of X -rays emitted) vs atomic mass is a straight line. Statement (II) : A plot of v(v = frequency of X -rays emitted) vs atomic number is a straight line. In the light of the above statements, choose the correct answer from the options given below : (1) Both Statement I and Statement II are true (2) Statement I is false but Statement II is true (3) Both Statement I and Statement II are false (4) Statement I is true but Statement II is false
Q62.If a0 is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength (λ) of the electron present in the second orbit of hydrogen atom? [n : any integer] (1) 8πa0 (2) 2a0 n nπ (3) 4n (4) 4πa0 πa0 n
Q33.An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then the radius of the electronic orbit in the first excited state is : (1) √ πeeBh (2) √2hπeB (3) √ 2πeBh (4) √4πeBh
Q68.Heat treatment of muscular pain involves radiation of wavelength of about 900 nm . Which spectral line of H atom is suitable for this? Given : Rydberg constant RH = 105 cm−1, h = 6.6 × 10−34 J s, c = 3 × 108 m/s ) (1) Balmer series, ∞→2 (2) Lyman series, ∞→1 (3) Paschen series, ∞→3 (4) Paschen series, 5 →3
Q26.During the transition of electron from state A to state C of a Bohr atom, the wavelength of emitted radiation is 2000Å and it becomes 6000Å when the electron jumps from state B to state C. Then the wavelength of the radiation emitted during the transition of electrons from state A to state B is (1) 4000Å (2) 2000Å (3) 3000Å (4) 6000Å
Q35.The number of spectral lines emitted by atomic hydrogen that is in the 4th energy level, is (1) 3 (2) 1 (3) 6 (4) 0
NCERT Chapters
- Class 12 Physics Ch 12: Atoms