Calculation of the Lowest Possible Frequency of Light to Ionize a Sodium Atom

In this article, we will guide you through the steps required to calculate the lowest possible frequency of light that can ionize a sodium atom. The ionization energy of a gaseous sodium atom is provided; we will use this information to find the minimum energy of the photon required to cause ionization. By understanding this process, you can gain insight into the relationship between photon energy, frequency, and ionization energy. Let's break it down step by step.

Given Information

It is given that one mole of sodium requires 495.5 KJ/mol to get ionized. This means 6.022 x 1023 atoms of sodium need 495.5 x 103 J of energy to get ionized. From this data, we can find out how much energy each sodium atom needs to get ionized.

Step 1: Calculate the Energy Required per Atom

The first step is to determine the energy required to ionize a single sodium atom. This can be calculated as follows:

( E_{text{per atom}} frac{495.5 times 10^3 text{ J/mol}}{6.022 times 10^{23} text{ atoms/mol}} )

( E_{text{per atom}} 8.22 times 10^{-19} text{ J} )

Step 2: Relate Photon Energy to Ionization Energy

When a single sodium atom is excited to ionize, it requires a single photon of light to provide the necessary energy. Therefore, the energy of the photon must equal the ionization energy of a single sodium atom, which is (8.22 times 10^{-19} text{ J}).

The relationship between the energy of a photon and its frequency is given by the equation:

( E h times f )

Where:

( E ) is the energy of the photon, ( h ) is Planck's constant, approximately (6.626 times 10^{-34} text{ Js}), ( f ) is the frequency of the photon.

Step 3: Calculate the Frequency of Light

Now we can rearrange the above equation to solve for the frequency:

( f frac{E}{h} )

Substitute the known values:

( f frac{8.22 times 10^{-19} text{ J}}{6.626 times 10^{-34} text{ Js}} )

( f 1.24 times 10^{15} text{ Hz} )

This is the lowest possible frequency of light that can ionize a sodium atom.

Conclusion

By understanding the relationship between the ionization energy, the energy of a photon, and the frequency of light, we have derived the lowest possible frequency of light that can ionize a sodium atom. This calculation can be useful in fields such as spectroscopy, atomic physics, and materials science.

Further Reading and Resources

If you are interested in learning more about this topic, we recommend the following resources:

Photon Energy - Wikipedia - Understanding the Relationship Relationship Between Wavelength and Frequency - Quora

These resources provide a deeper understanding of the relationship between photon energy, frequency, and wavelength.

If you have any questions or need further clarification, feel free to ask.