One line in the helium spectrum is bright yellow and has the wavelength $587.6 \mathrm{nm} .$ What is the difference in energy (in electron-volts) between two helium levels that produce this line?

Answer: To find the energy difference, follow these steps: 1. Convert the wavelength to frequency: \(f = \frac{3 \times 10^8 \ \mathrm{m/s}}{587.6 \times 10^{-9} \ \mathrm{m}}\) 2. Calculate the energy difference using Planck's equation: \(E = (6.626 \times 10^{-34} \ \mathrm{J \cdot s}) \times (\frac{3 \times 10^8 \ \mathrm{m/s}}{587.6 \times 10^{-9} \ \mathrm{m}})\) 3. Convert the energy difference to electron-volts: \(E_{\mathrm{eV}} = (6.626 \times 10^{-34} \ \mathrm{J \cdot s}) \times (\frac{3 \times 10^8 \ \mathrm{m/s}}{587.6 \times 10^{-9} \ \mathrm{m}}) \times \frac{6.242 \times 10^{18} \ \mathrm{eV}}{\mathrm{1 \ J}}\) Calculate the final expression to get the energy difference between the two helium levels in electron-volts.