3.Suppose the innermost orbit an electron can occupy has an energy level of -19 eV. Based on the absorption spectrum shown below, what is the energy of energy level 4?
To determine the energy of energy level 4, we need to understand the relationship between energy levels in an atom.
1. Start by understanding the concept of energy levels in an atom: In an atom, electrons occupy specific energy levels or shells. The energy levels are labeled using numbers or letters (such as 1, 2, 3, or K, L, M) in increasing order from the nucleus outward.
2. Understanding the energy levels of the electrons: The energy of an electron depends on its energy level. As the electron moves farther away from the nucleus, its energy increases. The energy levels of electrons are quantized, meaning they can only have certain specific values.
3. Using the given information: We know that the energy of the innermost orbit (energy level 1) is -19 eV. Since we want to find the energy of energy level 4, we need to calculate the difference in energy between energy level 4 and energy level 1.
4. Calculate the energy difference: The energy difference between energy level 4 and energy level 1 can be calculated by subtracting the energy of energy level 1 from the energy of energy level 4.
5. Energy level difference formula: The energy difference between two energy levels (ΔE) can be calculated using the formula ΔE = -13.6/n^2 (where n is the energy level number).
6. Plug in the values: In this case, we want to calculate the difference between energy level 4 and energy level 1, so we plug in the values as follows:
ΔE = -13.6/4^2 - (-13.6/1^2)
ΔE = -13.6/16 - (-13.6/1)
ΔE = -0.85 eV - (-13.6 eV)
ΔE = -0.85 eV + 13.6 eV
ΔE = 12.75 eV
Therefore, the energy of energy level 4 is 12.75 eV.