Atomic Spectra

To find the energy difference between the two energy levels in sodium responsible for emitting a spectral line at 589.6 nm, we use the relationship between energy, frequency, and wavelength given by the formula:

Energy (E) = h × c / λ

Where:

• h = Planck's constant = 6.626 × 10^-34 J·s
• c = Speed of light in a vacuum = 3.00 × 10⁸ m/s
• λ = Wavelength = 589.6 nm = 589.6 × 10^-9 m

Substitute these values into the formula to find the energy:

E = (6.626 × 10^-34 J·s) × (3.00 × 10⁸ m/s) / (589.6 × 10^-9 m)

E ≈ 3.37 × 10^-19 J

To convert this energy from joules to electronvolts (eV), use the conversion factor:

• 1 eV = 1.602 × 10^-19 J

Thus,

E ≈ 3.37 × 10^-19 J / 1.602 × 10^-19 J/eV

E ≈ 2.1 eV

Therefore, the difference in energy between the two energy levels is 2.1 eV, which matches the correct answer.