Energy is emitted by one excited sodium atom when it generates a photon?

[jewilki1]

Sodium vapor lamps are widely used for lighting public areas such as parking lots by emiting 589 nm yellow light.
a. how much energy is emitted by one excited sodium atom when it generates a photon?
b. How much energy is emitted when 1.00 mole of sodium atoms each generate a photon?
Can you help me with this problem. I am studying for a quiz.

How do you work this problem? This comes from problems of the day. We do not get answers or how to work them out. We are just supposed to study them after we work them. Thanks.

 

[sanitykey]

I think the answers may have something to do with the following equations:

[tex]E=hf[/tex]

Where E is the energy in joules, h is the Planck constant of [tex]6.63 \times 10^{-34}[/tex] joules per hertz, and f is the frequency of the em-radiation in hertz.

However you have the wavelength of the light not the frequency, but the two are related by:

[tex]c=f\lambda[/tex]

Where c is the speed of light (about [tex]3 \times 10^8[/tex]m/s), f is the frequency of the light in hertz and [tex]\lambda[/tex] is the wavelength of the light.

If you can find the answer to part a then for part b think about how many sodium atoms are in 1.00 mole.

I hope this helps jewilki1

 

[Blueshift5]

a. The energy emitted by one excited sodium atom when it generates a photon can be calculated using the formula E = hc/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength of the emitted photon. In this case, the wavelength is 589 nm, so we can plug in the values to get E = (6.626 x 10^-34 J*s)(3.00 x 10^8 m/s)/(589 x 10^-9 m) = 3.37 x 10^-19 J. This is the energy emitted by one excited sodium atom when it generates a photon.

b. To calculate the energy emitted when 1.00 mole of sodium atoms each generate a photon, we can use Avogadro's number (6.022 x 10^23 atoms/mol). This means that 1 mole of sodium atoms is equal to 6.022 x 10^23 atoms. So, if we multiply the energy calculated in part a by Avogadro's number, we get (3.37 x 10^-19 J)(6.022 x 10^23 atoms) = 2.03 x 10^5 J. This is the total energy emitted when 1.00 mole of sodium atoms each generate a photon.

To work this problem, you need to know the formula for calculating energy from wavelength, and the value of Avogadro's number. You also need to be able to convert units, as the wavelength given is in nanometers and the speed of light is in meters per second. Make sure to use the correct units in your calculations to get the correct answer.