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Worksheet: Quantum Particle in a Potential Well

Q1:

An electron confined to a box of width 0.15 nm by infinite potential energy barriers emits a photon when it makes a transition from the first excited state to the ground state. Find the wavelength of the emitted photon.

Q2:

An electron is confined to a box of width 0.250 nm. What is the wavelength of photons emitted when the electron transitions between the second excited state and the ground state?

Q3:

An electron is confined to a box of width 0.250 nm. What is the wavelength of photons emitted when the electron transitions between the third and second excited states?

Q4:

An electron is confined to a box of width 0.250 nm. What is the wavelength of photons emitted when the electron transitions between the fourth and second excited states?

Q5:

An electron in a long, organic molecule used in a dye laser behaves approximately like a quantum particle in a box with width 4.18 nm. Find the wavelength of the emitted photon when the electron makes a transition from the first excited state to the ground state.

Q6:

An electron in a long, organic molecule used in a dye laser behaves approximately like a quantum particle in a box with width 4.18 nm. Find the wavelength of the emitted photon when the electron makes a transition from the second excited state to the first excited state.

Q7:

Photons are emitted by an electron that is confined to a box. The longest wavelength of the emitted photons is 500 nm. What is the width of the box?

  • A 5 . 9 6 × 1 0 1 0 m
  • B 5 . 9 2 × 1 0 1 0 m
  • C 5 . 9 9 × 1 0 1 0 m
  • D 6 . 0 3 × 1 0 1 0 m
  • E 6 . 0 6 × 1 0 1 0 m

Q8:

What is the ground state energy of an alpha-particle confined to a one-dimensional box of length 15.0 fm?

Q9:

An electron confined to a box has a ground state energy of 2.5 eV. What is the width of the box?