# Solving Unexplained Homework Question: Sodium Emission Line at 589nm

• Sephiroth2088
In summary, the conversation discusses the energy produced by a certain number of excited sodium atoms with an emission line at 589nm. The answer is given as 5.481*10^4 and the conversation also poses questions about the energy of a single photon, the number of sodium atoms in a mole, and the number of sodium atoms in 0.2698 moles.
Sephiroth2088
Hello, I'm new and I have a question about something on my homework that I just can't find an explanation how to do.

if sodium has an emmsion line at 589nm, what is the energy (in joules) produced by 0.2698 moles of excited sodium atoms?

If anyone could tell me how to go from those above numbers to that answer I would sure appreicate it, thanks in advance.

1. What is the energy of a single photon with a wavelength of 589nm?
2. How many sodium atoms in a mole of sodium?
3. How many sodium atoms in 0.2698 moles of soduim?
4. Assuming each of the atoms is excited to the same level, how many 589nm photons are produced?

Hello there,

Firstly, we need to know the formula for calculating energy (in joules) of a photon emitted by an atom. It is given by E = hc/λ, where h is Planck's constant (6.626*10^-34 J*s) and c is the speed of light (3*10^8 m/s).

Next, we need to convert the wavelength from nanometers (nm) to meters (m) as the formula uses meters. This can be done by dividing the wavelength (589 nm) by 10^9. This gives us a value of 5.89*10^-7 m.

Now, we can plug in the values in the formula to get the energy of a single photon emitted by sodium atoms at 589 nm. This comes out to be 3.37*10^-19 J.

Since we are given the number of moles of excited sodium atoms (0.2698 moles), we need to multiply the energy of a single photon by Avogadro's number (6.022*10^23) to get the total energy produced by all the excited atoms.

Therefore, the final calculation would be 0.2698*6.022*10^23*3.37*10^-19 J, which gives us 5.481*10^4 J.

I hope this helps you understand the process of solving this question. If you have any further questions, please feel free to ask. Good luck with your homework!

## 1. What is a sodium emission line at 589nm?

A sodium emission line at 589nm is a specific wavelength of light that is emitted when an atom of sodium releases energy. This line is part of the visible spectrum and appears as a bright yellow color.

## 2. Why is the sodium emission line at 589nm important?

The sodium emission line at 589nm is important because it can be used to identify the presence of sodium in a substance. This is useful in various fields such as chemistry, astronomy, and environmental science.

## 3. How is the sodium emission line at 589nm calculated?

The wavelength of the sodium emission line at 589nm is calculated using the Rydberg formula, which takes into account the energy levels of the electrons in a sodium atom. The formula is: 1/λ = R(1/n1^2 - 1/n2^2), where λ is the wavelength, R is the Rydberg constant, and n1 and n2 are integers representing the energy levels of the electrons.

## 4. Can the sodium emission line at 589nm be seen with the naked eye?

Yes, the sodium emission line at 589nm can be seen with the naked eye. In fact, it is one of the brightest emission lines in the visible spectrum and is often used in streetlights and other types of lighting.

## 5. What are some real-world applications of the sodium emission line at 589nm?

The sodium emission line at 589nm has many real-world applications. It is used in spectroscopy to identify the presence of sodium in a sample, in astronomy to study the composition of stars and galaxies, and in environmental science to measure the amount of sodium in water and soil. It is also used in the manufacturing of streetlights and other types of lighting.

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