Question

calculating the wavelength of a spectral line from an energy diagram
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 b to a, 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 state. From the diagram, the energy of level A (ground state) is \(100\space zJ\).

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 \(500\space zJ\).

Step3: Determine photon absorption/emission

When an electron transitions from a higher energy level (B) to a lower energy level (A), it loses energy. This energy is released as a photon. So, a photon is emitted.

Step4: Calculate energy change

The energy change \(\Delta E=E_{B}-E_{A}\). Substituting the values, \(\Delta E = 500 - 100=400\space zJ\). Convert \(zJ\) to \(J\): \(1\space zJ = 1\times10^{-21}\space J\), so \(\Delta E=400\times10^{-21}\space J\).

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

We know \(h = 6.626\times10^{-34}\space J\cdot s\) and \(c = 3\times10^{8}\space m/s\). Rearranging the formula for \(\lambda\), we get \(\lambda=\frac{hc}{\Delta E}\).
Substitute the values: \(\lambda=\frac{6.626\times 10^{-34}\times3\times 10^{8}}{400\times10^{-21}}\).

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Answer:

100 zJ, 500 zJ, emitted, 497 nm