[Ishwar]

Electrons of energies 10.20 eV and 12.09 eV can cause radiations to be emitted from hydrogen atom. Calculate in each case the principle quantum number of the orbit to which the electron belongs and the wavelength of the radiations emitted if it drops back to its ground state.

How do i start this question? Thanks for all your help

[Yggdrasil]

Do you know the formual for the energy level of a hydrogen atom?

[Ishwar]

 

Do you know the formual for the energy level of a hydrogen atom?

well, I know that E_n = -13.6 x Z² / n² eV , where Z is the atomic number

but using this equation seems to give the incorrect answer

[Yggdrasil]

Can you show how you are getting this wrong answer?

Also, solving the second question might be easier.  Consider this:  it takes 13.6 eV to ionize an electron in the ground state.  If it takes only 10.20 eV to ionize a particular electron, what is this electron's energy relative to the ground state?  You can also think of it this way.  To ionize an electron, you could do it all at once by applying 13.6 eV or you could apply 13.6 eV it in two steps.  Lets say you apply X amount of energy to excite the electron to a level n.  Then you apply 10.20 eV to ionize the electron.  How would you find X?

[Ishwar]

Well, I know that E_n of one electron is 10.4 eV

so, using the formula for the energy of the electron,

10.4 = 13.6 x 1² / n²

making n the subject of the formula,

n = sqroot (13.6 / 10.4)
   = 1.1435... ??

[xiankai]

like Yggdrasil said,

E_n - E_x = (1/x² - 1/n²) x 13.6 x Z² eV

13.6 - 12.09 = 1/x² x 13.6 x Z²

x = 3 (roughly)

try doing the rest 

[Ishwar]

Thanks, i understand now