Q4. Use Balmer’s formula with R = 1.097 × 107 m−1 to find the wavelength of the hydrogen line for n = 5.
1/λ = 1.097 × 107 × (1/4 − 1/25) = 1.097 × 107 × 0.21 ≈ 2.30 × 106 m−1, so λ ≈ 434 nm, the violet-blue line (beyond the NCERT text).
Q5. Hydrogen at room temperature has nearly all its atoms in the ground state, and the smallest jump up from there needs 10.2 eV. What is the longest wavelength such hydrogen can absorb, and in which region is it?
λ = hc/E = (6.63 × 10−34 × 3 × 108)/
Q6. Find the frequency of hydrogen’s 656 nm line.
ν = c/λ = (3 × 108)/(656 × 10−9) ≈ 4.57 × 1014 Hz.
Q7. An astronomer finds dark lines at 656.3 nm and 486.1 nm in the spectrum of a star. What does this tell her?
These are hydrogen’s wavelengths, so the star’s outer layers contain hydrogen, hot enough for some atoms to be in the state just above the ground state. A gas’s absorption lines lie at wavelengths found in its emission spectrum, which identifies it (NCERT page 297; beyond the NCERT text for stars).