Question

this energy diagram shows the allowed energy levels of an electron in a certain atom or molecule:
use this diagram to complete the table below.
which is the ground state?
how many excited states are there?
how many lines are in the absorption line spectrum?
which transition causes the emission line at the shortest wavelength?
which transition causes the emission line at the longest wavelength?

Explanation:

Step1: Identify ground state

The ground state is the lowest - energy level. In the diagram, level A is the lowest.

Step2: Count excited states

Excited states are levels above the ground state. Levels B, C, and D are excited states. So there are \(3\) excited states.

Step3: Calculate absorption line spectrum

For absorption, the electron jumps from a lower to a higher energy level. The number of absorption lines is given by the combination formula \(n(n - 1)/2\) where \(n\) is the number of energy levels. Here \(n=4\), so \(4\times(4 - 1)/2=6\)

Step4: Determine shortest - wavelength emission

Emission occurs when an electron jumps from a higher to a lower energy level. The energy change \(\Delta E=E_{higher}-E_{lower}\). Using \(E = hc/\lambda\) (where \(h\) is Planck's constant and \(c\) is the speed of light), a larger \(\Delta E\) gives a shorter \(\lambda\). The largest energy change is \(D
ightarrow A\)

Step5: Determine longest - wavelength emission

The smallest energy change gives the longest wavelength. The smallest energy change is \(B
ightarrow A\)

Answer:

• Which is the ground state? \(A\)
• How many excited states are there? \(3\)
• How many lines are in the absorption line spectrum? \(6\)
• Which transition causes the emission line at the shortest wavelength? \(D

ightarrow A\)

• Which transition causes the emission line at the longest wavelength? \(B

ightarrow A\)