Question

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.

Answer 1

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

Step-by-step 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