Calculating the energy level and radius for a helium atom

[ttk3]

Homework Statement

Calculate the energy and radius for each of the five lowest (n = 1,2,3,4,5) electron orbits in a Helium atom with only one electron. Enter the energy as a positive value in units of "eV" and the radius in units of "nm". Hint: The Helium nucleus has 2 protons so Z = 2 and the ground state energy of Helium will be E0 = k(Ze)2/2r0.

Homework Equations

E = (E₀/n²)*Z²
E₀= 13.6 eV
Z²=4
r=(r₀/Z)*n²
Z=2

The Attempt at a Solution

I got the correct answers for n = 1-2 and 4-5, but I cannot get the right answer for n=3. could you check my work?

The answers I got were E = 6.044 eV and r = .238 nm

 

[G01]

I am getting the same numbers you are ttk3. The process for finding the answer for n=3 is the same as it is for the other four you got correct, so I don't see how you could get only n=3 incorrect.

Are you sure there isn't some error or typo in wherever you are getting the correct answer from?

 

[Moetasim]

for n=1
E = 1.511 eV and r = .596 nm for n=2
E = .671 eV and r = 1.336 nm for n=3
E = .377 eV and r = 2.372 nm for n=4
E = .241 eV and r = 3.784 nm for n=5



Your calculations seem to be correct. The only potential issue could be with the conversion of units. Make sure that your answers are in the correct units of eV for energy and nm for radius. Also, double check your calculations to ensure that they are accurate. If you are still having trouble with the n=3 calculation, try using a different approach or double check your equations to make sure they are being applied correctly. Overall, your answers for n=1-2 and 4-5 seem to be accurate, so it is likely just a minor error in your n=3 calculation. Keep up the good work!