When table salt is put in a candle flame, it burns bright yellow because of emission from the sodium atoms. This emission is at 590 nm. (a) What is the natural resonant frequency of the

sodium atom that produces this emission (i.e. what is the frequency of this light)? (b) What is the difference in energy between the two levels of the sodium atom that are responsible for this emission (i.e. what is the energy of a photon

speed = c = about3*10^8 m/s

distance=wave length= speed * time
frequency = 1/time

E = plank's constant * frequency

This is basic. Check your text!!!!

To answer these questions, we'll need to make use of some fundamental concepts in atomic physics and the electromagnetic spectrum.

(a) The frequency of light emitted by an atom is directly related to its resonant frequency, which is determined by the energy difference between the atom's energy levels. We can use the equation:

E = hf

where E is the energy of a photon, h is Planck's constant (approximately 6.626 x 10^-34 joule-seconds), and f is the frequency of light.

In this case, we are given the wavelength of the emitted light as 590 nm. We can convert this wavelength to frequency using the equation:

c = λf

where c is the speed of light (approximately 3 x 10^8 m/s) and λ is the wavelength.

Let's calculate the resonant frequency of the sodium atom:

First, convert the wavelength to meters:
λ = 590 nm = 590 x 10^-9 m

Now, rearrange the equation:
f = c/λ = (3 x 10^8 m/s) / (590 x 10^-9 m)

Calculate the frequency:
f ≈ 5.08 x 10^14 Hz

Therefore, the natural resonant frequency of the sodium atom that produces this emission is approximately 5.08 x 10^14 Hz.

(b) To find the energy difference between the two levels responsible for this emission, we can use the equation:

ΔE = hf = hc/λ

where ΔE is the energy difference, h is Planck's constant, c is the speed of light, and λ is the wavelength.

Plug in the values:
ΔE = (6.626 x 10^-34 J·s) × (3 x 10^8 m/s) / (590 x 10^-9 m)

Calculate the energy difference:
ΔE ≈ 3.37 x 10^-19 J

Therefore, the energy of a photon emitted by the sodium atom is approximately 3.37 x 10^-19 Joules.