Atomic Structure
- Energy and radius of first Bohr orbit of He^+ and Li^2+ are[Given R_H = 2.18×10^-18 J, a_0 = 52.9 pm] Answer: 1. E_n(mathrmLi²⁺) = -19.62×10⁻¹⁸ J; r_n(mathrmLi²⁺) = 17.6 pm; E_n(He^+) = -8.72×10⁻¹⁸ J; r_n(He^+) = 26.4 pm Key idea: for hydroge... 1
- The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes n=2 → n=3 and n=4 → n=6 transitions, respectively, is Answer: 4. 1/4 Key idea: absorbed wavelength is inversely proportional to the energy gap, 1/λ∝(1/n₁²-1/n₂²) . For 2→3 : 1/4-1/9=5/36 , so λ₁... 1
- The energy of an electron in the ground state (n = 1) for He^+ ion is -x J, then that for an electron in n = 2 state for Be^3+ ion in J is : Answer: 2. -x Key idea: for hydrogen-like ions E_n=-E₁(H) Z²/n² . For He^+ (Z=2), n=1: -x=-4E₀ , so E₀=x/4 . For mathrmBe³⁺ (Z=4), n=2: E=-E... 1
- Match List I with List II.List I (Quantum Number): A. m_l B. m_s C. l D. nList II (Information provided): I. shape of orbital II. size of orbital III. orientation of orbital IV. orientation of spin of electronChoose the correct answer from the option… Answer: 3. A-III, B-IV, C-I, D-II Key idea: each quantum number gives one property of the electron or orbital. m_l : orientation of the orbi... 1
- Select the correct statements from the following :A. Atoms of all elements are composed of two fundamental particles.B. The mass of the electron is 9.10939 × 10^-31 kg.C. All the isotopes of a given element show same chemical properties.D. Protons an… Answer: 1. B, C and E only Key idea: Check each statement. A. False: atoms are made of three fundamental particles (electron, proton, neutro... 1
- The relation between n_m, (n_m = the number of permissible values of magnetic quantum number (m)) for a given value of azimuthal quantum number (l), is Answer: 2. l = n_m - 1/2 Key idea: For a given l , m takes values from -l to +l including 0. Number of values: n_m = 2l + 1 . Rearranging, l... 1
- If radius of second Bohr orbit of the He^+ ion is 105.8 pm, what is the radius of third Bohr orbit of Li^2+ ion ? Answer: 2. 158.7 pm Key idea: Bohr radius r_n=0.529 n²/Z Å, so r∝ n²/Z . He^+ , n = 2: r=a₀×4/2=2a₀=105.8 pm, so a₀=52.9 pm. mathrmLi²⁺ , n... 1
- Identify the incorrect statement from the following. Answer: 1. The shapes of d_xy , d_yz , and d_zx orbitals are similar to each other ; and d_(x²-y²) and d_z² are similar to each other. Key i... 1
- A particular station of All India Radio, New Delhi, broadcasts on a frequency of 1,368 kHz (kilohertz). The wavelength of the electromagnetic radiation emitted by the transmitter is : [speed of light, c=3.0×10^8 ms^-1] Answer: 1. 219.3 m Key idea: λ=c/ν . ν=1368\ kHz=1.368×10⁶\ mathrms⁻¹ λ=3.0×10⁸/1.368×10⁶=219.3\ m . 1
- Choose the correct option for graphical representation of Boyle's law, which shows a graph of pressure vs. volume of a gas at different temperatures : Answer: 4. [graph option - see figure] Key idea: Boyle's law: PV=constant at fixed T, so P vs V is a rectangular hyperbola. A higher T gives... 1
- Which of the following series of transitions in the spectrum of hydrogen atom falls in visible region ? Answer: 2. Balmer series Balmer series (transitions to n = 2 from n = 3, 4, 5...) lies in the visible region (about 656 to 365 nm). Lyman is... 1
- 4d, 5p, 5f and 6p orbitals are arranged in the order of decreasing energy. The correct option is : Answer: 1. 5f > 6p > 5p > 4d Orbital energy in a many-electron atom follows the (n+l) rule; if (n+l) is equal, the orbital with lower n has... 1
- Which one is a wrong statement ? Answer: 2. The electronic configuration of N atom is1s ² 2s ² 2p _x¹ 2p _y¹ 2p _z¹ shown as orbital box diagram: 1s [up down], 2s [up down],... 1
- Which one is the wrong statement ? Answer: 3. The energy of 2s orbital is less than the energy of 2p orbital in case of Hydrogen like atoms. Key idea: in a hydrogen-like atom,... 1
- How many electrons can fit in the orbital for which n = 3 and l = 1? Answer: 4. 2 Key idea: one orbital holds at most 2 electrons (Pauli principle). n=3,l=1 is the 3p subshell, which has 3 orbitals (6 electron... 1
- Which of the following pairs of d-orbitals will have electron density along the axes? Answer: 2. d_z², d_(x²-y²) Key idea: d_z² and d_(x²-y²) have lobes along the axes; d_xy, d_yz, d_xz have lobes between the axes. So the pair... 1
- Two electrons occupying the same orbital are distinguished by : Answer: 4. Spin quantum number Key idea: two electrons in the same orbital have the same n, l and m. By the Pauli exclusion principle they m... 1