Bohr model, energy levels, hydrogen spectrum
- A model for quantized motion of an electron in a uniform magnetic field B states that the flux passing through the orbit of the electron is n(h/e) where n is an integer, h is Planck's constant and e is the magnitude of electron's charge. According to… Answer: 2. he/2π m Key idea: the electron moves in a circle in the field, and the given flux quantization fixes the orbit area. From evB=mv²... 1
- A particle of mass m is moving around the origin with a constant force F pulling it towards the origin. If Bohr model is used to describe its motion, the radius r of the n^th orbit and the particle's speed v in the orbit depend on n as Answer: 3. r ∝ n^(2/3);\ v ∝ n^(1/3) Key idea: apply Newton's second law with the constant force as the centripetal force, together with Boh... 1
- Match List I with List II.List I (Spectral Lines of Hydrogen for transitions from): A. n_2=3 to n_1=2; B. n_2=4 to n_1=2; C. n_2=5 to n_1=2; D. n_2=6 to n_1=2List II (Wavelengths (nm)): I. 410.2; II. 434.1; III. 656.3; IV. 486.1Choose the correct ans… Answer: 3. A-III, B-IV, C-II, D-I Key idea: These are Balmer lines (transitions to n=2 ); a larger jump means more energy and a shorter wave... 1
- The radius of inner most orbit of hydrogen atom is 5.3×10^-11 m. What is the radius of third allowed orbit of hydrogen atom? Answer: 1. 4.77 mathringA Bohr orbit radius: r_n=n² r₁ . Third orbit: r₃=9×5.3×10⁻¹¹=4.77×10⁻¹⁰ m = 4.77 Å (1 Å = 10⁻¹⁰ m). 1
- In hydrogen spectrum, the shortest wavelength in the Balmer series is λ. The shortest wavelength in the Bracket series is : Answer: 3. 4λ The shortest wavelength of a series comes from the transition from n=∞ to the series' lower level n₁ : dfrac1λ=R/n₁² , so λ∝ n... 1
- Let T_1 and T_2 be the energy of an electron in the first and second excited states of hydrogen atom, respectively. According to the Bohr's model of an atom, the ratio T_1 : T_2 is : Answer: 1. 9 : 4 In Bohr's model the energy magnitude is E_n∝ 1/n² . First excited state is n=2 and second excited state is n=3 . T₁/T₂=1/4/... 1
- For which one of the following, Bohr model is not valid ? Answer: 4. Singly ionised neon atom (Ne ^+ ) The Bohr model works only for one-electron (hydrogen-like) systems, where the electron feels ju... 1
- The total energy of an electron in an atom in an orbit is -3.4 eV. Its kinetic and potential energies are, respectively : Answer: 3. 3.4 eV, -6.8 eV For an electron in a bound orbit, KE=-E and PE=2E . With E=-3.4 eV: KE=+3.4 eV and PE=-6.8 eV. Check: 3.4-6.8=-3.... 1
- The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom, is Answer: 3. 1 : - 1 In a Bohr orbit, kinetic energy K=ke²/2r and potential energy U=-ke²/r . Total energy E=K+U=-ke²/2r=-K . K/E=K/-K=1:-1 1
- The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series is : Answer: 2. 4 Key idea: the last line of a series has n₂=∞ : dfrac1λ=RZ²(dfrac1n₁²-0) . Balmer ( n₁=2 ): dfrac1λ_B=R/4 . Lyman ( n₁=1 ): dfra... 1
- If an electron in a hydrogen atom jumps from the 3rd orbit to the 2nd orbit, it emits a photon of wavelength λ. When it jumps from the 4th orbit to the 3rd orbit, the corresponding wavelength of the photon will be Answer: 2. 20/7λ Use dfrac1λ=R(dfrac1n₁²-dfrac1n₂²) . 3 to 2: dfrac1λ=R(1/4-1/9)=5R/36 . 4 to 3: dfrac1λ'=R(1/9-dfrac116)=7R/144 . λ'/λ=5/36... 1
- Given the value of Rydberg constant is 10^7\ m^-1, the wave number of the last line of the Balmer series in hydrogen spectrum will be : Answer: 3. 0.25×10⁷\ m⁻¹ Key idea: barν=R(dfrac12²-dfrac1n²) ; the last Balmer line has n→∞ . barν=R/4=10⁷/4=0.25×10⁷\ m⁻¹ . 1