Construct an Energy-Level Diagram for Element with 1.66e-18 J Ionization Energy

[elliotyang]

Homework Statement

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.

Homework Equations

E=hf=hc/lamda

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

 

[Bacat]

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 $$E=\frac{hc}{\lambda}$$, 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.

 

[shamim khaliq]

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

 

[Evo]

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. ;)

 

[DeeNos]

because i dont know the value of the charge in the nucleus.

The energy-level diagram for this element would have the ground state at the bottom, with n=1, and the ionization energy at the top, with n=∞. The three longest wavelengths in the absorption spectrum correspond to the transitions from n=∞ to n=3, n=4, and n=5, respectively. The exact values of the energy levels cannot be determined without knowing the charge of the nucleus, but the general trend of increasing energy level spacing as n increases can still be shown. Additionally, the wavelengths given in the problem may not correspond exactly to the energy differences between the levels, as there may be other factors that affect the observed wavelengths in the absorption spectrum. Overall, the energy-level diagram for this element would show the energy levels increasing as n increases, with the ionization energy at the top and the three given wavelengths corresponding to transitions from the highest energy level down to lower levels.