Question

The sodium d-line is actually a pair of closely spaced spectroscopic lines seen in the emission spectrum of sodium atoms. The wavelengths are centered at 589.3 nm. The intensity of this emission makes it the major source of light (and causes the yellow color) in the sodium arc light.

(a) Calculate the energy change per sodium atom emitting a photon at the d-line wavelength.

Short answer

The energy change per sodium atom is$3.37\times {10}^{-9}\times \text{J}$

Step-by-step solution

Given data

The wavelength in the emission spectrum of sodium atoms is centered at 589.3 nm.

Formula used

The formula used to calculate the energy change per sodium atom which is emitting the photon at the d line wavelength is as follows:

$\mathbf{E}\mathbf{=}\frac{\mathbf{h}\mathbf{\times }\mathbf{c}}{\mathbf{\lambda }}$

Here:

Theplank constant (h) is 6.62607015×10⁻³⁴ j.s

The speed of light (c) is

The wavelength $\mathbf{\left(}\mathbf{\lambda }\mathbf{\right)}$ is 589.3 nm, which in meters is$5.893\times {10}^{-7}\text{m}$

Calculation

The values are put in the formula (stated above) to calculate the energy change per sodium atom as follows:

Therefore the energy change per sodium atom is $3.37\times {10}^{-9}\text{J}$