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

• elliotyang
In summary, the energy required to remove an electron from an atom or ion is called the ionization energy. The three longest wavelengths in an atom or ion's absorption spectrum are associated with the lowest energy levels. When n is increasing, the difference between energy levels would be smaller, so the three wavelengths would be emitted corresponding to the energy difference between ninfinity-ninifinity-1,ninfinity-ninifinity-2, and ninfinity-ninifinity-3. After doing all these, the student still cannot construct an energy diagram. The wavelengths probably correspond to orbital transitions of an electron that does not get ionized. Recognizing an orbital transition is lower energy than an ionization energy tells you which side of the
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.

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

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.

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

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. ;)

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.

1. What is an energy-level diagram for an element?

An energy-level diagram is a visual representation of the energy levels of an atom or element. It shows the different energy levels that an electron can occupy and the amount of energy required to move between these levels.

2. How is an energy-level diagram constructed?

An energy-level diagram is constructed by starting with the lowest energy level, known as the ground state, and then adding energy levels above it. Each energy level is represented by a horizontal line, and the energy of each level is shown on the vertical axis. The energy levels are typically labeled with the letters s, p, d, and f, corresponding to the different types of orbitals.

3. What does the ionization energy represent in an energy-level diagram?

The ionization energy is the amount of energy required to remove an electron from an atom or ion in its ground state. In an energy-level diagram, it is represented by the energy difference between the ground state and the first excited state. The ionization energy is a measure of how tightly an electron is held by the atom.

4. How is the ionization energy calculated for an element?

The ionization energy for an element is typically given in units of joules (J) or electron volts (eV). It can be calculated by measuring the energy required to remove an electron from the element and converting it to the desired units. For example, the ionization energy of an element with 1.66e-18 J ionization energy would be equal to 1.66 x 10^-18 J.

5. What information can be obtained from an energy-level diagram?

An energy-level diagram can provide information about an element's electronic structure, including the number of energy levels and the arrangement of electrons within these levels. It can also show the ionization energy and other energy transitions that an element undergoes. Additionally, an energy-level diagram can be used to predict an element's chemical properties and reactivity based on its electron configuration.

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