According to the equation for the Balmer line spectrum of hydrogen, a value of n = 3 gives a red spectral line at 656.3 nm, a value of n = 4 gives a green line at 486.1 nm, and a value of n = 5 gives a blue line at 434.0 nm. Calculate the energy in kilojoules per mole of the radiation corresponding to each of these spectral lines.

The Balmer series describes the wavelengths of light emitted by hydrogen when an electron transitions from a higher energy level (n ≥ 3) to the second energy level (n = 2). Each transition corresponds to a specific wavelength, producing visible spectral lines. The series is crucial for understanding the emission spectrum of hydrogen and is foundational in quantum mechanics.

The energy of a photon can be calculated using the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. This relationship shows that energy is inversely proportional to wavelength; shorter wavelengths correspond to higher energy photons. This concept is essential for calculating the energy associated with the spectral lines in the Balmer series.

To find the energy per mole of photons, the energy calculated for a single photon must be multiplied by Avogadro's number (approximately 6.022 x 10²³ mol⁻¹). This conversion is necessary to express energy in kilojoules per mole, which is a standard unit in chemistry for quantifying energy changes in reactions and processes involving large numbers of particles.