Title 02. STRUCTURE OF ATOM.pdf ✅

JEE JEE Advanced (2024) Q1 Rutherford’s experiment, which established the nuclear model of the atom, used a beam of (A) β-particles, which impinged on a metal foil and got absorbed (B) γ-rays, which impinged on a metal foil and got scattered (C) helium nuclei, which impinged on a metal foil and got scattered (D) None of these Q2 The first use of quantum theory to explain the structure of atom was made by (A) Heisenberg (B) Bohr (C) Planck (D) Einstein Q3 The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is (a is Bohr radius). (A) (B) (C) (D) Q4 At one time the meter was defined as 1650763.73 wavelength of the orange light emitted by a light source containing Kr atoms. What is the corresponding photon energy of this radiation? (A) 3.28 × 10 J/quanta (B) 1.2 × 10 J/quanta (C) 1.09 × 10 J/quanta (D) 2.048 J/quanta Q5 If l is the threshold wavelength for photoelectric emission from a metal surface, l is the wavelength of light falling on the surface of metal and m is the mass of electron, then the maximum speed of ejected electrons is given by (A) (B) (C) (D) Q6 The speed of electron revolving around H- nucleus is 0.547 × 10 m/s. The distance of electron from the nucleus is (A) 2.116 Å (B) 4.761 Å (C) 8.464 Å (D) 0.529 Å Q7 The time period of revolution in the third orbit of Li ion is x second. The time period of revolution in the second orbit of He ion should be (A) x s (B) (C) (D) Q8 The wavelengths of the first Lyman lines of hydrogen, He and Li ions are , , respectively. The ratio of these wavelengths is (A) 1 : 4 : 9 (B) 9 : 4 : 1 (C) 36 : 9 : 4 (D) 6 : 3 : 2 Q9 According to Bohr’s atomic theory, which of the following relations is/are correct? (A) Kinetic energy of electron (B) The product of speed of electron and the principal quantum number a z (C) Frequency of revolution of the electron in an orbit (D) Coloumbic force of attraction on the electron Q10 Which of the following statement(s) is/are correct? (A) The ratio of the radii of the first three Bohr orbits of hydrogen atom is 1 : 8 : 27. (B) The ratio of magnitude of total energy : kinetic energy : potential energy for electron in any orbit of hydrogen atom is 1 : 1 : 3. (C) The frequency of a green light is 6 × 10 Hz, then its wavelength is 500 nm. (D) The ratio of de Broglie wavelength of a H- atom, He-atom and CH – molecule moving with equal kinetic energy is 4 : 2 : 1. Q11 The frequency of certain line of the Lyman series (n = 4 to n = 1) of the atomic spectrum of hydrogen can satisfy the following conditions. Chemistry Atomic Structure h 2 4π 2ma2 0 h 2 16π 2ma2 0 h 2 32π 2ma 2 0 h 2 64π 2ma2 0 86 –19 –31 –27 0 [ ( − λ)] 2h m λ0 1/2 [ ( − λ)] 2hc m λ0 1/2 [ ( )] 2hc m λ0−λ λ0λ 1/2 [ ( − )] 2h m 1 λ0 1 λ 1/2 6 2+ + x s 3 2 x s 2 3 x s 2 3 + 2+ λ1 λ2 λ3 α z 2 n 2 2 α z 2 n 3 α z 2 n 4 14 4 2 1
JEE (A) It is the sum of the frequencies of a Lyman line and a Balmer line. (B) It is the sum of the frequencies of a certain Lyman line, a Balmer line and a Brackett line. (C) It is the sum of the frequencies of a Lyman line, a Balmer line and a Paschen line. (D) It is the sum of the frequencies of a Lyman and a Paschen line. Q12 Select the correct statement(s) among the following. (A) Outside of that orbital, the probability of finding the electron is zero. (B) For single electronic atom or ion, the most probable distance of electron in a orbital having no radial node is from the (C) The average distance of electron (belonging from the same orbit) from the nucleus decreases with increase in the value of angular momentum quantum number for the orbital. (D) The angular wave function of any s-orbital is independent from and . Q13 Among the following, select the correct information(s). (A) The opposite lobes in any d-orbital have the same sign of wave function. (B) 1s orbital is the only orbital for which the sign of wave function does not have radial as well as angular dependency. (C) The number of radial nodes is always greater than that of angular nodes. (D) All the orbitals belonging from an orbit have the same number of total nodes. Q14 The average life time for the n = 3 excited state of a hydrogen-like atom is 4.8 × 10 s and that for n = 2 state is 1.28 × 10 s. Ratio of the average number of revolutions made in the n = 3 state to the average number of revolutions made in the n = 2 state before any transition can take place from these state is 1 : x. The value of x is Q15 A sample of hydrogen atoms containing all the atoms in a particular excited state absorb radiations of a particular wavelength by which the atoms get excited to another excited state. When the atoms finally de-excite to the ground state, they emit the radiations of 10 different wavelengths. Out of these 10 radiations, 7 have wavelengths shorter than the absorbed radiation and 2 have wavelength longer than the absorbed radiation. The orbit number for the initial excited state of atoms is x, find x. Q16 The diameter of a dust particle of mass 10 g is 2 Å. The speed of this dust particle is measured with the uncertainty of The minimum uncertainty in measuring the position of the dust particle (in order of 10 m) is y. Find y Q17 The circumference of the second orbit of an atom or ion having single electron is 4 nm. The de Broglie wavelength of electron (in nm) revolving in this orbit is x then determine the value of x Q18 The Schrodinger wave equation for hydrogen atom is where a is Bohr’s radius. If the radial node of 2s be at r , then the value of is n 2a0 Z θ φ –8 –7 –3 × 3.313 π 10−3 –26 Ψ2s = (2 − ) 1 4√2π ( )1 a0 3/2 r0 a0 e − r0 a0 0 0 r0 a0
JEE Answer Key Q 1 ( C ) Q 2 ( C ) Q 3 ( C ) Q 4 ( A ) Q 5 ( C ) Q 6 ( C ) Q 7 ( C ) Q 8 ( C ) Q 9 ( A, C, D ) Q10 ( C, D ) Q11 ( A, C, D ) Q12 ( B, C, D ) Q13 ( A, B, D ) Q14 (09.00) Q15 (03.00) Q16 (05.00) Q17 (02.00) Q18 (02.00)