Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Energy-level diagram

  1. Feb 7, 2009 #1
    1. The problem statement, all variables and given/known data
    An element has an ionization energy of 1.66 × 10-18 J. The three longest wavelengths in its absorption spectrum are 253.7 nm, 185.0 nm and 158.5 nm.

    Construct an energy-level diagram for this element.

    2. Relevant equations


    3. The attempt at a solution
    ionisation energy is the energy required to remove 1 mol of electron from 1 mol of gaseous atom or ion. So the energy different between the two states is between n=? and n=infinity right? i cannot calculate the exact value using rydberg equation because i do not know the element, so cannot plug in the value of the charge in nucleus.
    longest wavelengths indicates smallest energy.
    when n is increasing, the difference between energy level would be smaller.
    so i suppose these three wavelengths are emitted due to the energy difference between ninfinity-ninifinity-1,ninfinity-ninifinity-2, ninfinity-ninifinity-3

    so how should i proceed after this?
    after doing all these, i still cannot construct energy diagram
  2. jcsd
  3. Feb 10, 2009 #2
    The wavelengths probably correspond to orbital transitions of an electron that does not get ionized, so your energy diagram is just showing the relative spacing of the different transitions. You're supposed to recognize that an orbital transition is lower energy than an ionization energy, so that tells you which side of the diagram they go on. Using your equation [tex]E=\frac{hc}{\lambda}[/tex], you discover that transitions of longer wavelength have lower energy. You can actually calculate this transition energy using the equation.

    Once you have the energy of each transition and the ionization energy you can construct a simple diagram that shows the relative spacing of these transitions.

    It's true that you can consider n going to infinity before ionization, but also remember that the relative spacing between the transitions is getting infinitely small in that limit. So just call the ionization energy the limit and find the relative spacings of the energy levels.

    I hope this helps.
  4. Nov 10, 2014 #3
    my answer is:
    E=hc/λ so E= 6.63e-34 x 3.0e8 /λ = 1.989e-25/λ
    Eorbital1-Eorbital0=7.84e-19 J
    Eorbital2-Eorbital0=1.08e-18 J
    Eorbital3-Eorbital0=1.25e-18 J

    Eionisation= 1.66 × 10-18J... we make this zero and compare how much energy it would take to get an electron to this energy
    Eorbital1 - Eionisation=7.839968466693e-19-1.66e-18=-8.76e-19 J
    Eorbital2- Eionisation=1.075135135135e-18-1.66e-18=-5.85e-19 J
    Eorbital3- Eionisation=1.2548895899e-18-1.66e-18=-4.05e-19 J

    see final answer in attached picture answerQ4.jpg
  5. Nov 10, 2014 #4


    User Avatar

    Staff: Mentor

    Please remember not to give out answers to homework, it's against our rules, although this thread being 5 years old, I doubt that they are still waiting. ;)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?