Numericals
Worked solutions for the examples and calculation questions in this chapter.
READY TO GO BEYOND · ATOMS IN A SHEET OF PAPER
Atoms ≈ thickness / diameter = 10⁻⁴ m ÷ 10⁻¹⁰ m = 10⁶
AVERAGE ATOMIC MASS OF CHLORINE
35 × 75/100 + 37 × 25/100 = 26.25 + 9.25 = 35.5 u
PAUSE AND PONDER 10 · ATOMIC NUMBER 26, 56 NUCLEONS
Electrons = protons = 26; neutrons = 56 − 26 = 30
PAUSE AND PONDER 11
Neutrons = 41 − 20 = 21
PAUSE AND PONDER 12
Mass number = 18 + 17 = 35
PAUSE AND PONDER 13
11 electrons means 11 protons.
Neutrons = 23 − 11 = 12
PAUSE AND PONDER 18 · BROMINE
79 × 49.7/100 + 81 × 50.3/100 = 39.26 + 40.74 ≈ 80 u
REVISE, REFLECT, REFINE 8 · MAGNESIUM
Protons = Z = 12; electrons = 12; neutrons = 24 − 12 = 12
Electronic configuration: K = 2, L = 8, M = 2
REVISE, REFLECT, REFINE 11
Atom 70X with 31 electrons has 31 protons.
Neutrons = 70 − 31 = 39
REVISE, REFLECT, REFINE 12 · GOLD
Neutrons = 197 − 79 = 118; electrons = 79
REVISE, REFLECT, REFINE 14 · ELEMENT X
Protons = A − n = 35 − 18 = 17 = electrons = Z
X is chlorine, with configuration 2, 8, 7 and 7 valence electrons. Adding two neutrons gives mass number 37; the new atom is an isotope of X.
REVISE, REFLECT, REFINE 15 · HEAVIER ELECTRONS
Replacement particles of mass 500 × the electron mass: 12 × 500 ≈ 6000 electron masses ≈ 3.3 proton masses.
Atomic number and mass number do not change (they count protons and nucleons); the atomic mass increases by about 3.3 u; overall charge stays zero.
NCERT Q&A
Answers to the Pause and Ponder questions and the Revise, Reflect, Refine exercises. Numerical working is in the Numericals tab.
Pause and Ponder
PAUSE AND PONDER 1
In a clay-and-beads model of Thomson's atom, what happens if (i) the positive charge on the clay is less than the total negative charge of the beads, (ii) the clay itself carries a bit of negative charge?
Answer: (i) The model would have a net negative charge, so it would not represent a neutral atom. (ii) Likewise, the model would not be neutral unless the positive charge equals the total negative charge, so it would not represent a neutral atom.
PAUSE AND PONDER 2
Could an orange or lemon be a good comparison for Thomson's model?
Answer: It matches partly: the seeds are scattered in a soft pulp, like electrons in a positive sphere. It falls short because seeds are few and large, while real electrons are tiny and equal in number to the positive charge, and the pulp is not actually charged.
PAUSE AND PONDER 3
Why did Thomson conclude that electrons are present in all atoms?
Answer: Cathode rays were the same whatever the cathode material or the gas in the tube, so electrons must come from the atoms of every element.
PAUSE AND PONDER 4
What would happen if α-particles were replaced with negatively charged particles in Rutherford's experiment?
Answer: Negative particles would be attracted by the positive nucleus (bending towards it) and repelled by electrons, so the pattern of scattering would differ. They would not be repelled sharply away from the nucleus as α-particles are.
PAUSE AND PONDER 5
How does the fact that a few α-particles bounced back rule out the plum pudding model?
Answer: Bouncing back needs a very strong repulsion from a heavy, concentrated positive charge. In Thomson's model the positive charge is spread evenly and is too weak to turn back a fast α-particle.
PAUSE AND PONDER 6
What one question would you ask Rutherford?
Answer: Open-ended. For example: "How did you decide that the nucleus is so small compared to the atom?" (Any sensible question is acceptable.)
PAUSE AND PONDER 7
Assertion: Rutherford concluded that most of the mass of an atom is in the nucleus. Reason: According to Thomson's model, electrons are embedded in a uniformly distributed positive sphere.
Answer: (ii) Both A and R are true, but R is not the correct explanation of A.
PAUSE AND PONDER 8
Name a new element after yourself and justify the symbol using IUPAC rules.
Answer: Open-ended. For example, "Xyzium" with symbol Xy: the first letter is capital and the second is small, both taken from the name.
PAUSE AND PONDER 9
What problems could arise if every scientist used different symbols for the same element?
Answer: Scientists across the world could not communicate clearly; formulae and equations would be confusing and open to errors.
PAUSE AND PONDER 10
An atom with atomic number 26 has 56 nucleons. Find the number of electrons, protons and neutrons.
Answer: 26 electrons, 26 protons and 30 neutrons.
PAUSE AND PONDER 11
The nucleus has 20 protons and mass number 41. Find the number of neutrons.
Answer: 21 neutrons.
PAUSE AND PONDER 12
An atom has 18 neutrons and atomic number 17. What is its mass number?
Answer: 35.
PAUSE AND PONDER 13
An atom 23A has 11 electrons. Find the number of neutrons.
Answer: 12 neutrons (11 protons, 23 − 11 = 12).
PAUSE AND PONDER 14
Number of electrons in the outermost shell of (i) C-12, (ii) F-19, (iii) Si-28.
Answer: (i) 4 (2,4). (ii) 7 (2,7). (iii) 4 (2,8,4).
PAUSE AND PONDER 15
Electronic configuration of the elements with atomic numbers 12, 16 and 18.
Answer: 12: 2, 8, 2. 16: 2, 8, 6. 18: 2, 8, 8.
PAUSE AND PONDER 16
Riddle: mass number 23, 11 protons, soft metal reacting vigorously with water.
Answer: Sodium (Na), with 12 neutrons.
PAUSE AND PONDER 17
Two atoms have 11 protons each, but 12 and 13 neutrons. Compare their atomic and mass numbers. Same or different elements?
Answer: Both have atomic number 11; the mass numbers are 23 and 24. They are the same element (sodium) and are isotopes.
PAUSE AND PONDER 18
Calculate the average atomic mass of bromine: 79Br (49.7%) and 81Br (50.3%).
Answer: About 80 u (79 × 0.497 + 81 × 0.503 = 80.0 u).
Revise, Reflect, Refine
QUESTION 1
Choose the correct statements about Rutherford's gold foil experiment.
Answer: (ii) and (iii) are correct. (i) is incorrect: neutrons were discovered by Chadwick in 1932. (iv) is incorrect: the large deflection of a few α-particles showed a small, dense, positive nucleus; it did not show how electrons move.
QUESTION 2
Correct or incorrect according to Bohr's model?
Answer: (i) Incorrect: electrons do not lose energy in their fixed orbits. (ii) Incorrect: electrons move only in fixed energy levels. (iii) Correct: they revolve in orbits of fixed energy without losing energy. (iv) Incorrect: electrons cannot be found between energy levels.
QUESTION 3
Nuclei X (18 p, 19 n), Y (17 p, 18 n), Z (17 p, 20 n). Relation between Y and Z, and Z and X?
Answer: (i) Y and Z have the same atomic number (17) but different mass numbers (35 and 37): they are isotopes. (ii) Z (A = 37) and X (A = 37) have the same mass number but different atomic numbers (17 and 18): they are isobars.
QUESTION 4
What did Rutherford conclude from the α-particles that bounced back or deflected at large angles?
Answer: The positive charge of the atom is concentrated in a very small, dense region at the centre (the nucleus) that holds most of the mass. A fast α-particle is turned back only when it meets this heavy positive centre.
QUESTION 5
Arrange the models in chronological order.
Answer: (iv) Dalton: indivisible atoms; (ii) Thomson: plum pudding; (iii) Rutherford: dense nucleus; (i) Bohr: fixed orbits with definite energy. Each model explained something the earlier one could not.
QUESTION 6
Why do orbiting electrons not fly away from the atom? What keeps them attracted?
Answer: The electrostatic attraction between the negatively charged electrons and the positively charged protons in the nucleus keeps them in orbit.
QUESTION 7
Assertion: the discovery of subatomic particles helped in understanding the atomic structure. Reason: the number of electrons equals the number of protons in an atom.
Answer: (ii) Both are true, but R does not explain A.
QUESTION 8
Magnesium: mass number 24, atomic number 12. Find protons, neutrons, electrons and the arrangement.
Answer: 12 protons, 12 neutrons, 12 electrons; electrons arranged 2, 8, 2 in the K, L, M shells.
QUESTION 9
For the elements in Fig. 8.17, find name, symbol, electrons, valence electrons, valency, protons, atomic number.
Answer: (a) Lithium, Li, 3, 1, 1, 3, 3. (b) Nitrogen, N, 7, 5, 3, 7, 7. (c) Aluminium, Al, 13, 3, 3, 13, 13. (d) Fluorine, F, 9, 7, 1, 9, 9.
QUESTION 10
Why did Rutherford's model fail to explain stability while Bohr's succeeded?
Answer: In Rutherford's model an orbiting electron is accelerating and should lose energy and spiral into the nucleus. Bohr introduced stationary states: in these fixed orbits the electron does not lose energy, so the atom is stable.
QUESTION 11
An atom 70X has 31 electrons. How many neutrons?
Answer: 39.
QUESTION 12
79 protons and mass number 197: number of neutrons and electrons?
Answer: 118 neutrons and 79 electrons.
QUESTION 13
Complete Table 8.5.
Answer: Z = 5: A = 11, p = 5, e = 5, Boron. Nitrogen: Z = 7, n = 7, p = 7. A = 24, p = 12: Z = 12, n = 12, e = 12, Magnesium. Z = 15, n = 16: A = 31, p = 15, e = 15, Phosphorus. A = 1, n = 0: Z = 1, p = 1, e = 1, Hydrogen.
QUESTION 14
Element X: mass number 35, 18 neutrons. Find electrons, protons, atomic number, identity, configuration, valence electrons, new mass number, relation.
Answer: (i) 17 electrons and 17 protons. (ii) 17. (iii) Chlorine. (iv) 2, 8, 7. (v) 7. (vi) 37. (vii) The new atom is an isotope of X.
QUESTION 15
Electrons replaced by particles with the same charge but 500 times heavier. Effect on atomic number, atomic mass, mass number, overall charge?
Answer: (i) Atomic number: no change (12 protons). (ii) Atomic mass: increases (by about 3.3 u). (iii) Mass number: no change. (iv) Overall charge: no change (still neutral).