How to calculate the kinetic energy, energy and frequency? [ENDORSED]

[Chem_Mod]

Light hits a sodium metal surface and the velocity of the ejected electron is 6.61 x 105 m.s-1. The work function for sodium is 150.6 kJ.mol-1.

Answer the following three questions.
A. What is the kinetic energy of the ejected electron?
B. How much energy is required to remove an electron from one sodium atom?
C. What is the frequency of the incident light on the sodium metal surface? If you can, could you give me a step by step explanation on how to solve this?

[Chem_Mod]

The steps to solve the problem are:
1. Use Ek = 1/2 mv^2 2.

2. Divide the total energy (work function) by Avogadro's number.

3. Use: kinetic energy of e- = energy of incoming photon – work function ****In addition to covering this in class, the course reader has detailed examples as does the textbook.

[derek1d]

Won't the mass of the electron need to be given in order to solve A) of this problem?

[diegomartinez1F]

Mass of electron is given:

Me= 9.10938 x 10^-31 kg

[Jacinda Wollenweber 1D]

The steps to solve the problem are:
1. Use Ek = 1/2 mv^2 2.

2. Divide the total energy (work function) by Avogadro's number.

3. Use: kinetic energy of e- = energy of incoming photon – work function ****In addition to covering this in class, the course reader has detailed examples as does the textbook.

Why do we have to divide the work function by Avogrado's number? I thought the energy was given simply by adding the kinetic energy and threshold energy together.

[Sarah_Wilen]

This is because the work function's energy is given in kJ/mol. You need to solve for the energy of a single unit. That was very poorly explained, sorry. Refer to this other answer:
viewtopic.php?f=14&t=21193

[Kevin Morden 1E]

Mass of electron is given:

Me= 9.10938 x 10^-31 kg

Is the mass of an electron always going to be the same?

[Chem_Mod]

Yes, the mass of an electron is always going to be the same.

[Sohini Halder 1G]

As Dr. Lavelle said in lecture, it always helps to write out the equation in words first.
For example:
Energy of incoming photon = Workfunction of metal (or energy needed to remove electron) + Kinetic energy of the electron emitted
After this, you can rearrange whatever way you need to for the problem.

[Kevin Hernandez 3A]

The steps to solve the problem are:
1. Use Ek = 1/2 mv^2 2.

2. Divide the total energy (work function) by Avogadro's number.

3. Use: kinetic energy of e- = energy of incoming photon – work function ****In addition to covering this in class, the course reader has detailed examples as does the textbook.

For Part c, would you subtract the work function of the sodium metal or subtract the work function of the one sodium atom?

[gabbym]

This was so helpful, thank you!

[Ashley P 4I]

At last I finally understood what this problem was asking, thank you so much!

[Liza Hayrapetyan-3K]

Thank you so much! This was extremely helpful.

[Andrew Bennecke]

Thank you, I was genuinely confused about this topic as well!

[Yiting_Gong_4L]

Thank you for this explanation! This was very helpful.

[AustinMcBrideDis3L]

Mass of electron is given:

Me= 9.10938 x 10^-31 kg

Do we need to convert this to grams or can we keep it as kg?

[Moura Girgis 1F]

Mass of electron is given:

Me= 9.10938 x 10^-31 kg

Do we need to convert this to grams or can we keep it as kg?

We need to keep it in kg, as all of the other units include kg, such as Joules (kg.m^2/s^2)

[clairehathaway 2J]

Won't the mass of the electron need to be given in order to solve A) of this problem?

This might be kinda obvious, but kinetic energy only applies to electrons right? So whenever we use the equation
the m will always represent the mass of an electron?

[Chudi Onyedika 3A]

Won't the mass of the electron need to be given in order to solve A) of this problem?

This might be kinda obvious, but kinetic energy only applies to electrons right? So whenever we use the equation
the m will always represent the mass of an electron?

The kinetic energy equation can be applied to any object, but in this case, the mass should represent the mass of an electron.

[Giselle_zamora_1L]

So for part A, are there any additional steps to take after doing the 1/2 mv? Because I did that and I got a fairly large number that wasn't any of the options but I don't know where I went wrong.

The steps to solve the problem are:
1. Use Ek = 1/2 mv^2 2.

2. Divide the total energy (work function) by Avogadro's number.

3. Use: kinetic energy of e- = energy of incoming photon – work function ****In addition to covering this in class, the course reader has detailed examples as does the textbook.

For Part c, would you subtract the work function of the sodium metal or subtract the work function of the one sodium atom?

[Giselle_zamora_1L]

for part B, is there any particular reason why we should divide by Avogadro's number? I thought that the work function was the minimum amount needed to free the electron so that it would be a given?

The steps to solve the problem are:
1. Use Ek = 1/2 mv^2 2.

2. Divide the total energy (work function) by Avogadro's number.

3. Use: kinetic energy of e- = energy of incoming photon – work function ****In addition to covering this in class, the course reader has detailed examples as does the textbook.

For Part c, would you subtract the work function of the sodium metal or subtract the work function of the one sodium atom?

[sadiebrebes]

Mass of electron is given:

Me= 9.10938 x 10^-31 kg

Where is this given? Do we just look up the mass of sodium metal? Or is it supposed to be in the questions?

Thank you

[Giselle Simmons 2D]

For A, how do the units work out to be Joules for the answer?

[Giselle Simmons 2D]

For B, I was a bit confused but here is how to do it.
First, convert 150.6 KJ/mol (given) to Joules by multiplying it by 1000L/1 KJ. This should give you 1.506 x 10^5 J.
Then, divide 1.506 x 10^5 J by Avogrado's number, which is 6.02 x 10^23 mol.
The answer is 2.501 x 10^-19 Joules.

[Minoo Bastani 2J]

Mass of electron is given:

Me= 9.10938 x 10^-31 kg

Where is this given? Do we just look up the mass of sodium metal? Or is it supposed to be in the questions?

Thank you

The mass of an electron is a constant value, because it is unchanging even in different atoms. I believe it is featured on the constant sheet that Dr.Lavelle provides for the midterms and final, so take it as a value that is never going to change. It was not given directly in the problem because it is assumed that you have access to the constants that you need.

[PranavKetharam]

for part B, is there any particular reason why we should divide by Avogadro's number? I thought that the work function was the minimum amount needed to free the electron so that it would be a given?

The steps to solve the problem are:
1. Use Ek = 1/2 mv^2 2.

2. Divide the total energy (work function) by Avogadro's number.

3. Use: kinetic energy of e- = energy of incoming photon – work function ****In addition to covering this in class, the course reader has detailed examples as does the textbook.

For Part c, would you subtract the work function of the sodium metal or subtract the work function of the one sodium atom?

Since the question is specifically asking for the energy from one sodium atom, we have to use Avogadro's number. This is because the work function is represented as 150.6 KJ.mol^-1. Avogadro's number represents the number of atoms in a mole of a substance; therefore, dividing the work function by Avogadro's number is a requirement to accurately identify the energy from one sodium atom.