More practice questions

4. Q4. Show that the de Broglie wavelength of the electron in the nth Bohr orbit is proportional to n.

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   λ_n = 2πr_n/n, and r_n = n²a₀, so λ_n = 2πna₀ ∝ n. Equivalently, λ = h/mv and v ∝ 1/n (reasoned from NCERT Eqs. (12.7) and (12.12)).

5. Q5. Find the ratio of the de Broglie wavelengths of the electron in the n = 1 and n = 3 orbits of hydrogen.

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   λ ∝ n, so λ₁ : λ₃ = 1 : 3 (reasoned from NCERT Eqs. (12.7) and (12.12)).

6. Q6. Why was it natural for Bohr to quantise angular momentum rather than some other quantity?

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   Planck’s constant h has the dimensions of angular momentum, J s = kg m^² s^⁻¹, and for circular orbits angular momentum is a very relevant quantity (NCERT Points to ponder 2, page 304).

7. Q7. Name the two limitations of the Bohr model that NCERT lists.

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   It cannot be extended to atoms with two or more electrons, such as helium, and it cannot explain the relative intensities of the lines in the hydrogen spectrum (NCERT page 302).