Question

use this diagram to complete the table below.
what is the energy of the electron in the ground state? zj
what is the energy of the electron in the first excited state? zj
if the electron makes the transition shown by the red arrow, from a to c, will a photon be absorbed or emitted? absorbed emitted
calculate the wavelength of the photon that would be absorbed or emitted. round your answer to 3 significant digits. nm

Explanation:

Step1: Determine ground - state energy

The ground state is the lowest energy level. From the diagram, the energy of level A (ground state) is \(200\ \text{zJ}\).

Step2: Determine first - excited state energy

The first excited state is the next higher energy level. From the diagram, the energy of level B (first excited state) is \(300\ \text{zJ}\).

Step3: Determine photon absorption/emission

When an electron moves from a lower energy level (A) to a higher energy level (C), it needs to gain energy. So, a photon is absorbed.

Step4: Calculate energy change

The energy change \(\Delta E=E_{C}-E_{A}\). From the diagram, \(E_{C} = 500\ \text{zJ}\) and \(E_{A}=200\ \text{zJ}\), so \(\Delta E=(500 - 200)\ \text{zJ}=300\ \text{zJ}=300\times10^{- 21}\ \text{J}\) (since \(1\ \text{zJ}=10^{-21}\ \text{J}\)).
We use the formula \(E = hc/\lambda\), where \(h = 6.626\times10^{-34}\ \text{J}\cdot\text{s}\) and \(c = 3\times10^{8}\ \text{m/s}\).
Rearranging for \(\lambda\), we get \(\lambda=\frac{hc}{\Delta E}\).
Substitute the values: \(\lambda=\frac{6.626\times 10^{-34}\times3\times 10^{8}}{300\times10^{-21}}\)

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Answer:

Question	Answer
What is the energy of the electron in the first excited state?	\(300\ \text{zJ}\)
If the electron makes the transition shown by the red arrow, from A to C, will a photon be absorbed or emitted?	absorbed
Calculate the wavelength of the photon that would be absorbed or emitted. Round your answer to 3 significant digits.	\(663\ \text{nm}\)