Q4. Estimate the mass of 1 cm3 of nuclear matter.
m = ρV ≈ 2.3 × 1017 × 10−6 ≈ 2.3 × 1011 kg, about 230 million tonnes packed into a sugar cube (reasoned from NCERT page 309).
Q5. Estimate the ratio of the radius of a gold-197 nucleus to the radius of a gold atom, taking the atom to be about 10−10 m across.
R ≈ 7.0 × 10−15 m, and the atom’s radius is about 0.5 × 10−10 m, so the ratio is about 1.4 × 10−4, of the order of 10−4, as NCERT says (NCERT pages 306 and 309).
Q6. By what factor does the surface area of a nucleus grow when A goes from 27 to 216?
R ∝ A1/3, so R doubles (216/27 = 8, and 81/3 = 2), and the surface area, ∝ R2, grows 4 times (reasoned from NCERT Eq. (13.5), page 309).
Q7. Why do electron-scattering and alpha-scattering experiments give slightly different nuclear radii?
Electrons sense how the charge of the nucleus is spread out, while alpha particles sense the nuclear matter itself (NCERT Points to ponder 2, page 320).
Q8. Why is the density of a whole atom not independent of its size, though the density of its nucleus is?
An atom is mostly empty space around its nucleus, and the size of the electron cloud does not grow in step with the mass; only nuclear matter is packed at a fixed density (NCERT Points to ponder 1, page 320; NCERT page 309).