Finding the wave length incident light troubles wee

[mr_coffee]

hello everyone!
I'm having some troubles figuring out what I'm doing wrong here.
The problem says:
Light strikes a sodium surface, causing photoelectric emission. The stopping potential for the ejected electrons is 6.1 V, and the work function of sodium is 2.2 eV. What is the wavelength of the incident light?
it wants the answer in nm as well, i submitted:
2.39277E-17 nm which was wrong

Here is how i got that answer:
let f equal frequencey;
let L = wave length;
h is planks constant which is:
6.62E-34 Js
f = (6.1 + 2.2)/h;
f = 1.25E34;
L = c/f, where c is the speed of light.
c = 3E8 m/s;

I figured out the fequencey so:
L = 3E8/(1.25E34);
L = 2.39277E-26m;
it wants it in nano meters so i divided it by E-9;
L = 2.39277E-17 nm;

Any ideas where i screwed up? Thanks!

I'm thinking its wrong because the 2.2 units are eV, not V. I know 1eV = 1.6E-19J, but that would just convert 2.2 into jouls, not volts.

EDIT:
I got it, i just had to convert planks constant to eVs instead of Js.

 

[anathema]

So the final equation was:
L = (3E8 * 6.626E-34)/(1.25E34 * 1.6E-19);
L = 3.177E-7 m = 317.7 nm

Hi there! It looks like you were on the right track, but there were a couple of small errors in your calculations. First, as you mentioned, the work function of sodium is given in eV, so it needs to be converted to joules before using it in any equations. This can be done by multiplying by the conversion factor of 1.6E-19 J/eV. So the work function should be 2.2 * 1.6E-19 = 3.52E-19 J.

Next, you correctly calculated the frequency using the stopping potential and work function, but you used the incorrect value for Planck's constant. The value of 6.62E-34 J*s is for Planck's constant in SI units, but since we are using energy in electron-volts, we need to use the value of 4.14E-15 eV*s. So the frequency should be (6.1 + 3.52) / (4.14E-15) = 2.03E36 Hz.

Finally, to find the wavelength, we can use the formula c = fλ, where c is the speed of light (3E8 m/s). So the wavelength is c / f = (3E8) / (2.03E36) = 1.48E-28 m. To convert to nanometers, we can multiply by 1E9 to get 1.48E-19 nm, which is approximately 148 nm.

I hope this helps clear up any confusion and helps you with your calculations in the future. Keep up the good work!

 

[kyle8921]

Hi there! It looks like you were on the right track with your calculations, but there are a few errors that led to your incorrect answer. First, as you mentioned, the work function of sodium is given in units of eV, not V. This means that you need to convert it to joules before using it in your equation. As you correctly pointed out, 1 eV is equal to 1.6E-19 J, so the work function of sodium is actually 3.52E-19 J. This will change your calculated frequency and therefore your wavelength.

Another issue is with your use of Planck's constant. In this case, you need to use the value of Planck's constant in units of eV*s, not Js. This is because the work function is given in eV, so all of your units need to be consistent. Planck's constant in eV*s is 4.14E-15 eV*s.

Fixing these two errors, your final calculated wavelength should be 4.67E-7 nm. I hope this helps and good luck with your problem!