Question

this energy diagram shows the allowed energy levels of an electron in a certain atom. (note: the si prefix zepto means ( 10^{-21} ). you can find the meaning of any si prefix in the aleks data tab.)
use this diagram to complete the table below.
what is the energy of the electron in the ground state?
what is the energy of the electron in the first excited state?
if the electron makes the transition shown by the red arrow, from a to b, will a photon be absorbed or emitted?
calculate the wavelength of the photon that would be absorbed or emitted. round your answer to 3 significant digits.

Explanation:

Step1: Determine the energy of the electron in the ground state

The ground - state is the lowest energy state. From the diagram, the energy of the electron in the ground state (A) is \(300\space zJ\).

Step2: Determine the energy of the electron in the first excited state

The first excited state is the next higher energy state. From the diagram, the energy of the electron in the first excited state (B) is \(600\space zJ\).

Step3: Determine if the photon is absorbed or emitted

When an electron moves from a lower energy state (A) to a higher energy state (B), it absorbs energy. So, a photon will be absorbed.

Step4: Calculate the energy change \(\Delta E\)

\(\Delta E=E_{final}-E_{initial}\)
\(\Delta E = 600\space zJ - 300\space zJ=300\space zJ\)

Step5: Use the formula \(E = hc/\lambda\) to find the wavelength \(\lambda\)

We know that \(h = 6.626\times10^{-34}\space J\cdot s\), \(c = 3\times10^{8}\space m/s\), and \(E = 300\times10^{-21}\space J\) (since \(1\space zJ= 10^{-21}\space J\))
\(\lambda=\frac{hc}{E}\)
\(\lambda=\frac{6.626\times 10^{-34}\times3\times 10^{8}}{300\times10^{-21}}\)
\(\lambda=\frac{19.878\times10^{-26}}{300\times10^{-21}}\)
\(\lambda = 6.626\times10^{-7}\space m\)
To convert to nanometers (\(1\space m = 10^{9}\space nm\))
\(\lambda=663\space nm\)

Answer:

• What is the energy of the electron in the ground state? \(300\space zJ\)
• What is the energy of the electron in the first excited state? \(600\space zJ\)
• If the electron makes the transition shown by the red arrow, from A to B, will a photon be absorbed or emitted? Absorbed
• Calculate the wavelength of the photon that would be absorbed or emitted. \(663\space nm\)