Tiêu đề 02. STRUCTURE OF ATOM - 2 (2).pdf ✅

1 JEE ADVANCED 2024 Atomic Structure Single Correct (1 – 9) 1. Two carbon discs, 1.0 g each are 1.0 cm apart have equal and opposite charges. If the force of attraction between them is 10−5 N, then the ratio of excess electrons to the total atoms on the negatively charged disc is (NA = 6 × 1023 , e = 1.6 × 10−19C) (1) 2.4 × 10−12: 1 (2) 10−14: 2.4 (3) 1012: 2.4 (4) 2.4: 1012 2. The ratio of the speed of the electron in the first Bohr orbit of hydrogen and the speed of light is equal to (where e, h and c have their usual meanings) (1) 2πhc/e 2 (2) e 2 c/2πh (3) e 2h/2πc (4) e 2/2ε0hc 3. In a discharge tube, there are only two hydrogen atoms. If the electrons in both atoms are de-exciting from 4th orbit, the minimum and maximum number of spectral lines should, respectively, be (1) 1,4 (2) 4,1 (3) 3,4 (4) 1,6 4. The wavelengths of the first Lyman lines of hydrogen, He+ and Li2+ ions are λ1, λ2, λ3 . The ratio of these wavelengths is (1) 1:4:9 (2) 9:4:1 (3) 36:9:4 (4) 6:3:2 5. A single electron species in energy level (orbit number n ) with energy X was provided with excess of energy so that it jumps to higher energy level with energy Y. If it can emit radiations of six different wavelengths on de-excitement between these two energy levels, then the correct relation is (1) X Y = (n − 1) 2 (2) X Y = 1 + 3 n (3) √ X Y = 1 + 3 n (4) X Y = 1 + n 3 6. What should be the increase in kinetic energy of electron in order to decrease its de Broglie wavelength from 100 nm to 50 nm ? (1) 0.451keV (2) 4.51 × 10-4 eV (3) 4.51 × 10-3 eV (4) 0.0451eV 7. The minimum uncertainty in de Broglie wavelength of an electron accelerated from rest by a potential difference of 6.0 V, if the uncertainty in measuring the position is 1/π nm, is (1) 6.25Å (2) 6.0Å (3) 0.625 Å (4) 0.3125 Å 8. The magnitude of the orbital angular momentum of an electron is given by L = √5 h/π. How many orbitals of this kind are possible, belonging to an orbit? (1) 4 (2) 5 (3) 11 (4) 9 9. Which of the following graph represents the radial probability function of 3d electron? (1) (2) (3) (4) DPP - 2
2 One or more than one correct 10. Which of the following statement(s) is/are correct? (1) The ratio of the radii of the first three Bohr orbits of hydrogen atom is 1:8:27. (2) The ratio of magnitude of total energy : kinetic energy : potential energy for electron in any orbit of hydrogen atom is 1:1:2. (3) The frequency of a green light is 6 × 1014 Hz, then its wavelength is 500 nm. (4) The ratio of de Broglie wavelength of a H- atom, He-atom and CH4-molecule moving with equal kinetic energy is 4:2:1. 11. Which of the following suggested that de Broglie wavelengths is not possible for the electron in a Bohr's orbit of the hydrogen atom? (1) 3.20Å (2) 4.98 Å (3) 9.96 Å (4) 6.64 Å 12. Which of the following information is true? (1) 3s orbital is spherically symmetrical with two nodes. (2) dx 2−y 2 orbitals has lobes of electron density in XY-plane along X and Y-axis. (3) The radial probability curve of 1s, 3p and 5d have one, two and three regions of maximum probability. (4) 3dz 2 has zero electron density in XY-plane. 13. The angular part of the wave function depends on the quantum numbers (1) n (2) l (3) m (4) s Comprehension: 1 A certain gas of identical hydrogen-like atoms has all its atoms in a particular upper energy level. The atoms make transition to a higher level when a monochromatic radiation having wavelength 1654 Å is incident on it. Subsequently, the atoms emit radiation of only three different photon energies. 14. The initial energy level of atoms was (1) n=1 (2) n=2 (3) n=3 (4) n=4 15. The final energy level of atoms is (1) n=1 (2) n=2 (3) n=3 (4) n=4 16. The atom/ion is (1) H (2) D (3) He+ (4) Li+2 17. The energy of photon required to remove electron from higher energy level is (1) 6.04eV (2) 13.6eV (3) 27.2eV (4) 36.8eV Comprehension: 2 A hydrogen-like atom of atomic number Z is in an excited state of quantum number 2n. It can emit a maximum energy photon of 204eV. If it makes a transition to quantum state n, a photon of energy 40.8eV is emitted. 18. What is the initial excited state of the atom? (1) 4 (2) 8 (3) 16 (4) 2 19. What is the value of Z ? (1) 2 (2) 4 (3) 8 (4) 16 20. What is the energy of ground state of this atom? (1) -13.6eV (2) -54.4eV (3) -217.6eV (4) -870.4eV 21. What is the minimum energy of the photons emitted by this atom during de-excitation? (1) 204eV (2) 4.16eV (3) 10.6eV (4) 13.6eV Integer Type Questions – Single Digit (0–9) 22. The quantum number n corresponding to the excited state of He+ ion if on transition to the ground state that ion emits two photons in succession with wavelengths 108.5 and 30.4 nm is 23. The atomic number of hydrogen-like ion has the wavelength difference between the first line of Balmer and Lyman series equal to 59.3 nm. 24. The diameter of a dust particle of mass 10−3 g is 2 Å. The speed of this dust particle is measured with the uncertainty of 3.313 π × 10−3 m/s. The minimum uncertainty in measuring the position of the duct particle (in order of 10−26 m ) is 25. The uncertainty in position and velocity of a particle are 10−11 m and 5.27 × 10−24 m ⋅ s −1 , respectively. The minimum mass of the particle (in kg ) is Matrix – Match Type Questions
3 26. Match the columns. (A) 3s (P) (B) 4s (Q) (C) 2p (R) (D) 3p (S) (1) A → P; B → S, C → Q, D → R (2) A → R; B → S, C → Q, D → P (3) A → P; B → R, C → Q, D → S (4) A → Q; B → P, C → R, D → S 27. Match Column I with Column II in hydrogen atom spectrum. Column I Column II (A) Orbital with (P) 3dx 2−y 2 radial and angular. nodes (B) Orbitals with (Q) 2pZ number of radial nodes less than the number of angular nodes. (C) Orbitals with (R) 3px zero radial nodes but two angular nodes. (S) 5dxy (1) A → R, S; B → Q, P; C → P (2) A → R, S; B → P, Q, ; C → P, R (3) A → R, Q; B → S, P; C → P (4) A → R, S; B → Q, P; C → S
4 Answer Key 1 . ( 2 ) 2 . ( 4 ) 3 . ( 1 ) 4 . ( 3 ) 5 . ( 3 ) 6 . ( 2 ) 7 . ( 3 ) 8 . ( 4 ) 9 . ( 1 ) 10 . ( 2, 3, 4 ) 11 . (1, 2 ) 12 . (1, 2, 3 ) 13 . ( 2, 3 ) 14 . ( 2 ) 15 . ( 3 ) 16 . ( 3 ) 17 . ( 1 ) 18 . ( 1 ) 19 . ( 2 ) 20 . ( 3 ) 21 . ( 3 ) 22 . ( 5 ) 2 3 . ( 3 ) 2 4 . ( 5 ) 2 5 . ( 1 ) 2 6 . ( 1 ) 2 7 . ( 1 )