Q4. Choose the correct words (NCERT Exercise 12.1): (a) The size of the atom in Thomson’s model is ____ the atomic size in Rutherford’s model (much greater than / no different from / much less than). For (b) to (d), choose from Thomson’s model / Rutherford’s model. (b) In the ground state of ____ electrons are in stable equilibrium, while in ____ electrons always feel a net force. (c) A classical atom based on ____ is doomed to collapse. (d) An atom has a nearly continuous mass distribution in ____ but a highly non-uniform one in ____. (e) The positively charged part of the atom has most of the mass in ____ (Rutherford’s model / both the models).
Using the equilibrium assumptions in the textbook comparison (not a claim of full classical stability): (a) No different from. (b) Thomson’s model; Rutherford’s model. (c) Rutherford’s model. (d) Thomson’s model; Rutherford’s model. (e) Both the models (NCERT Exercise 12.1, page 305; answer on page 351).
Q5. The kinetic energy of the alpha particles is doubled. What happens to the distance of closest approach? What is it for a silver nucleus (Z = 47) compared with gold (Z = 79) at the same energy?
d = 2Ze/(4πεK) is proportional to Z/K. Doubling K halves d. At the same K, silver gives 47/79 ≈ 0.59 times the distance for gold (reasoned from NCERT Example 12.2, page 295).
Q6. A 7.7 MeV alpha particle is scattered through 90° by a gold nucleus. What was its impact parameter?
b = (d/2) cot(θ/2), and cot 45° = 1, so b = d/2. With d ≈ 30 fm (NCERT Example 12.2, page 295), b ≈ 15 fm (beyond the NCERT text).
Q7. A small detector at fixed distance and acceptance solid angle counts 400 alpha particles a minute at 90°. About how many would it count at 60°, using Rutherford’s 1/sin(θ/2) law?
The ratio is sin45°/sin30° = 0.25/0.0625 = 4, so about 1600 a minute (beyond the NCERT text).
Q8. Why do the atomic electrons hardly deflect the alpha particles?
An alpha particle, 6.64 × 10−27 kg, is about 7300 times as heavy as an electron, 9.11 × 10−31 kg, so collisions with electrons barely change its motion (NCERT page 293; the alpha particle’s mass is from NCERT’s answer to Exercise 12.2, page 351).