Q4. Assertion: an electron and a proton with the same nonrelativistic kinetic energy have different de Broglie wavelengths. Reason: λ = h/√(2mK) depends on the mass. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: at the same K the heavier proton has the larger momentum and so the shorter wavelength (reasoned from NCERT Eq. (11.5), page 285; λ = h/√(2mK) is beyond the NCERT text).
Q5. Through what potential difference must an electron be accelerated from rest to have a de Broglie wavelength of 0.10 nm?
λ ≈ 1.227/√V nm gives √V ≈ 12.27, so V ≈ 150 V (beyond the NCERT text).
Q6. A nonrelativistic particle’s speed is doubled. What happens to its de Broglie wavelength? What if its kinetic energy is doubled instead?
Doubling the speed doubles p, so λ halves. Doubling K multiplies p by √2, so λ falls by a factor √2 (reasoned from NCERT Eq. (11.5), page 285).
Q7. How fast must an electron move to have the same wavelength as a photon of 500 nm?
p = h/λ is the same for both, so v = h/(mλ) = (6.63 × 10−34)/
Q8. A proton and an alpha particle are accelerated from rest through the same potential difference. Find λp/λα.
λ = h/√(2mqV). The alpha particle has about 4 times the mass and 2 times the charge, so λp/λα = √(4 × 2) = 2√2 ≈ 2.8 (beyond the NCERT text).