Atoms and Nuclei
- 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
- Given below are two statements :Statement I : Atoms are electrically neutral as they contain equal number of positive and negative charges.Statement II : Atoms of each element are stable and emit their characteristic spectrum.In the light of the abov… Answer: 4. Statement I is correct but Statement II is incorrect. Key idea: Check each statement on its own. Statement I: An atom has equal n... 1
- ^290_82X α Y e^+ Z β^- P e^- QIn the nuclear emission stated above, the mass number and atomic number of the product Q respectively, are : Answer: 1. 286, 81 Key idea: α emission lowers A by 4 and Z by 2; β^+ (positron) lowers Z by 1; β^- (electron) raises Z by 1. The mass numbe... 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
- The half life of a radioactive substance is 20 minutes. In how much time, the activity of substance drops to ≤ft(1/16)^th of its initial value? Answer: 1. 80 minutes Activity falls by half every half-life. dfrac116=(1/2)⁴ , so 4 half-lives are needed. t=4×20=80 minutes. The answer is... 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
- A nucleus of mass number 189 splits into two nuclei having mass number 125 and 64. The ratio of radius of two daughter nuclei respectively is : Answer: 4. 5 : 4 Nuclear radius is R=R₀A^(1/3) . R₁/R₂=(125/64)^(1/3)=5/4 The ratio is 5:4 . Option (4). 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
- In the given nuclear reaction, the element X is :^22_11Na → X + e^+ + Answer: 4. ²²₁₀Ne The emission of a positron is beta-plus decay: a proton turns into a neutron, so the mass number stays the same and the at... 1
- A radioactive nucleus ^A_ZX undergoes spontaneous decay in the sequence^A_ZX → _Z-1B → _Z-3C → _Z-2D, where Z is the atomic number of element X. The possible decay particles in the sequence are : Answer: 3. β^+, α, β^- Key idea: α decay lowers Z by 2; β^- raises Z by 1; β^+ lowers Z by 1. Z→ Z-1 : β^+ . Z-1→ Z-3 : α . Z-3→ Z-2 : β^- .... 1
- The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be : Answer: 2. 1/2√(2) Key idea: activity decays as A=A₀(1/2)^t/T_(1/2) . dfrac AA₀=(1/2)^(150/100)=(1/2)^(3/2)=dfrac12sqrt2 . Option 2. 1
- A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding energy per nucleon of unfragmented nuclei is 7.6 MeV while that of fragments is 8.5 MeV. The total gain in the Binding Energy in the process is : Answer: 4. 216 MeV Key idea: gain in binding energy = total B.E. of fragments - B.E. of parent. 240×7.6=1824 MeV; fragments: 240×8.5=2040 Me... 1
- When a uranium isotope ^235_92U is bombarded with a neutron, it generates ^89_36Kr, three neutrons and : Answer: 1. ¹⁴⁴₅₆ Ba Balance mass number and atomic number. Left: ²³⁵₉₂U+¹₀n gives A=236,\ Z=92 . Right: ⁸⁹₃₆Kr+3 ¹₀n+^A_Z X . A=236-89-3=144... 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 energy equivalent of 0.5 g of a substance is : Answer: 2. 4.5×10¹³ J Use Einstein's mass-energy relation E=mc² . E=0.5×10⁻³×(3×10⁸)²=4.5×10¹³\ J Answer: option 2. Remember to convert gram... 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
- α-particle consists of : Answer: 1. 2 protons and 2 neutrons only An α -particle is the nucleus of a helium atom, ⁴₂He : 2 protons and 2 neutrons, with no electrons. 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
- For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is Answer: 1. 20 If 450 of 600 nuclei disintegrate, 150 remain, which is 1/4 of the original. N/N₀=(1/2)ⁿ=1/4⇒ n=2 half-lives. Time =2×10=20 mi... 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
- Radioactive material 'A' has decay constant '8λ' and material 'B' has decay constant 'λ'. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A' will be 1/e ? Answer: 1. 1/7λ Key idea: N=N₀e^(-λ t) for each material, and take the ratio of the two. N_A=N₀e^(-8λ t) , N_B=N₀e^(-λ t) . Then N_A/N_B=e^(... 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