## Dino Nuggets question 8b

Ryan Juncker 3D
Posts: 51
Joined: Wed Sep 18, 2019 12:18 am

### Dino Nuggets question 8b

I was going back and doing Dino nuggets (the midterm review) number 8b and think I did the right conversion and formula but have gotten the wring answer multiple times. Can anyone help me out on this?

Posts: 52
Joined: Thu Jul 11, 2019 12:16 am
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### Re: Dino Nuggets question 8b

Unless you provide the formulas/conversions you used, it will be difficult to help, but in the meantime, here's a couple points to consider. Are all your units correct? You need to convert the work function of sodium to kJ/electron at the very least. Also, are you keeping in mind that the energy of the electron cannot be found using E = hv because electrons have mass?

Sebastian Lee 1L
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### Re: Dino Nuggets question 8b

For reference: 8b) A newly designed laser pointer with a certain frequency is pointed at a sodium metal surface. An electron is ejected from the metal surface with wavelength 1.10 nm. What is the frequency of the light from the laser pointer? The work function of sodium is 150.6 kJ∙mol-1.

I'll just outline the main steps to the problem and maybe you can see where you went wrong.

So you probably know the equation for the photoelectric effect: Energy of photon - work function (aka energy to remove electron) = kinetic energy of ejected electron
The problem is asking us for the frequency of the light from the laser pointer so we should be looking to solve for the energy of the photon.

First, you'll need to find the kinetic energy of the ejected electron. The problem states that the ejected electron has a wavelength of 1.10 nm. If we know the wavelength, we can find out the velocity of the electron using the deBroglie equation: . Remember that you MUST use deBroglie to find the wavelength of anything with mass. Wavelength * frequency = speed of light can only work for, well, light. Solving for velocity you should get 6.61 * 105 m/s. Once you know velocity, you can find the kinetic energy using: E=(1/2)mv2. Solving this you should find the kinetic energy of the electron to be 1.99 * 10-19 J.

Next, you'll want to find the work function/threshold energy of the sodium. The problem gives it to you in kJ/mol. Each photon will excite one atom's electron so you want to find the work function in units of J/atom. Using 1000J = 1 kJ and 1 mol = 6.022 * 1023 atoms, you should find a threshold energy of 2.501 * 10-19J.

So from here, you can find the energy of the photon which will be the kinetic energy of the electron plus the work function. Adding the two, you'll get 4.49 * 10-19 J as the energy of the photon. Since we know that for light, E=hv, you can find the frequency to be 6.78 * 1014 Hz.

Angela Patel 2J
Posts: 110
Joined: Sat Aug 24, 2019 12:17 am

### Re: Dino Nuggets question 8b

Sebastian Lee 1H wrote:For reference: 8b) A newly designed laser pointer with a certain frequency is pointed at a sodium metal surface. An electron is ejected from the metal surface with wavelength 1.10 nm. What is the frequency of the light from the laser pointer? The work function of sodium is 150.6 kJ∙mol-1.

I'll just outline the main steps to the problem and maybe you can see where you went wrong.

So you probably know the equation for the photoelectric effect: Energy of photon - work function (aka energy to remove electron) = kinetic energy of ejected electron
The problem is asking us for the frequency of the light from the laser pointer so we should be looking to solve for the energy of the photon.

First, you'll need to find the kinetic energy of the ejected electron. The problem states that the ejected electron has a wavelength of 1.10 nm. If we know the wavelength, we can find out the velocity of the electron using the deBroglie equation: . Remember that you MUST use deBroglie to find the wavelength of anything with mass. Wavelength * frequency = speed of light can only work for, well, light. Solving for velocity you should get 6.61 * 105 m/s. Once you know velocity, you can find the kinetic energy using: E=(1/2)mv2. Solving this you should find the kinetic energy of the electron to be 1.99 * 10-19 J.

Next, you'll want to find the work function/threshold energy of the sodium. The problem gives it to you in kJ/mol. Each photon will excite one atom's electron so you want to find the work function in units of J/atom. Using 1000J = 1 kJ and 1 mol = 6.022 * 1023 atoms, you should find a threshold energy of 2.501 * 10-19J.

So from here, you can find the energy of the photon which will be the kinetic energy of the electron plus the work function. Adding the two, you'll get 4.49 * 10-19 J as the energy of the photon. Since we know that for light, E=hv, you can find the frequency to be 6.78 * 1014 Hz.

Thank you so much for the detailed answer! I was having trouble with this question and this helped me get the right answer.