Worksheet: Spontaneous and Stimulated Emission

In this worksheet, we will practice describing the processes of spontaneous emission of light and stimulated emission of light.

Q1:

Which of the following is the closest value to the approximate typical lifetime of an excited electron in an atom?

  • A0.1 ms
  • B1 µs
  • C0.1 ns
  • D10 µs
  • E10 ns

Q2:

The diagram shows the ground state and the excited state of an electron in an atom that is in the path of a stream of photons. Which of the following diagrams most correctly represents the stimulated emission of a photon from the atom due to a change in the energy level of the electron?

  • A
  • B
  • C
  • D

Q3:

At an instant 𝑡, a hydrogen atom has just absorbed a photon, increasing the energy of its electron to 𝐸. A time interval Δ𝑡1µs then elapses, during which no other photons interact with the atom.

How does 𝐸, the energy of the electron at a time Δ𝑡 after 𝑡, compare to 𝐸?

  • A𝐸>𝐸
  • B𝐸=𝐸
  • C𝐸<𝐸

Will any photons have been emitted at a time Δ𝑡 after 𝑡?

  • AYes
  • BNo

Which of the following is the term used for the state of the electron at a time Δ𝑡 after 𝑡?

  • ASpontaneous
  • BExcited
  • CRelaxed
  • DInstantaneous
  • EStimulated

Q4:

At an instant 𝑡, a photon 𝛾 has just been absorbed by an atom that contains many electrons that can occupy various energy states. At an instant 𝑡=𝑡+Δ𝑡, Δ𝑡10 s, the atom has emitted two photons, 𝛾 and 𝛾. Between 𝑡 and 𝑡, the atom does not interact with any other photons. No photons are emitted other than 𝛾 and 𝛾.

How does the energy of 𝛾 compare to that of 𝛾?

  • A𝛾<𝛾
  • B𝛾>𝛾
  • C𝛾=𝛾

How does the energy of 𝛾 compare to that of 𝛾?

  • A𝛾=𝛾
  • B𝛾<𝛾
  • C𝛾>𝛾

Q5:

At an instant 𝑡, a photon 𝛾 is absorbed by the electron in a hydrogen atom. The electron is in a relaxed state before 𝑡. At an instant 𝑡, a photon 𝛾 that has an energy equal to that of 𝛾 interacts with the electron. The interval between 𝑡 and 𝑡0.1ns. A second time interval then elapses, during which a photon 𝛾 is emitted. No photons are absorbed or emitted other than 𝛾 and 𝛾, and no photons other than 𝛾 and 𝛾 interact with the electron.

What is the ratio of the energy of 𝛾 to the energy of 𝛾?

If the direction of travel of 𝛾 just before 𝑡 is defined as being along the 𝑥-axis in the positive direction, which of the following could be the direction of travel of 𝛾 when it is emitted?

  • AIn a direction between the direction of the 𝑥-axis and a direction perpendicular to the 𝑥-axis
  • BAlong the 𝑥-axis in the positive direction
  • CAlong the 𝑥-axis in the negative direction
  • DPerpendicular to the 𝑥-axis

Which of the following is the full range of Φ, the possible phase difference between 𝛾 at 𝑡 and 𝛾 when it is emitted?

  • A0Φ𝜋2radrad
  • B0Φ2𝜋radrad
  • C0Φ𝜋4radrad
  • D0Φ𝜋radrad
  • E0Φ0radrad

Which of the following is the term used for the type of photon emission that produces 𝛾?

  • ASpontaneous
  • BRelaxed
  • CExcited
  • DStimulated
  • EInstantaneous

Q6:

At an instant 𝑡, a photon 𝛾 is absorbed by the electron in a hydrogen atom. The electron is in a relaxed state before 𝑡, and its energy after 𝛾 is absorbed is 𝐸. At an instant 𝑡, a photon 𝛾 that has an energy equal to that of 𝛾 is absorbed by the electron. The interval between 𝑡 and 𝑡0.1ns. A second time interval 1µs then elapses, after which the energy of the electron is 𝐸. No photons are absorbed or emitted other than 𝛾 and 𝛾. How does 𝐸 compare to 𝐸?

  • A𝐸<𝐸
  • B𝐸=𝐸
  • C𝐸>𝐸

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