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. McMurry, John E ... Chemistry (p. 189). Pearson Education. Kindle Edition.

E3 = 3.03 10⁻¹⁶ kJ, E4 = 4.09 10⁻¹⁶ kJ and E5 = 4.58 10⁻¹⁶ kJ

Explanation:

They give us some spectral lines of the Balmer series, let's take the opportunity to place the values in SI units

n = 3 λ = 656.3 nm = 656.3 10⁻⁹ m

n = 4 λ = 486.1 nm = 486.1 10⁻⁹ m

n = 5 λ=434.0 nm = 434.0 10⁻⁹ m

Let's use the Planck equation

E = h f

The speed of light equation

c = λ f

replace

E = h c / λ

Where h is the Planck constant that is worth 6.63 10⁻³⁴ J s and c is the speed of light that is worth 3 10⁸ m / s

Let's calculate the energies

E = 6.63 10⁻³⁴ 3 10⁸ / λ

E = 19.89 10⁻²⁶ / λ

n = 3

E3 = 19.89 10⁻²⁶ / 656.3 10⁻⁹

E3 = 3.03 10⁻¹⁹ J

1 kJ = 10³ J

E3 = 3.03 10⁻¹⁶ kJ

n = 4

E4 = 19.89 10⁻²⁶ / 486.1 10⁻⁹

E4 = 4.09 10⁻¹⁹ J

E4 = 4.09 10⁻¹⁶ kJ

n = 5

E5 = 19.89 10⁻²⁶ / 434.0 10⁻⁹

E5 = 4.58 10⁻¹⁹ J

E5 = 4.58 10⁻¹⁶ kJ