# Standing Waves & The Schrödinger Equation

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## Standing Waves & The Schrödinger Equation Answer Key

1.

Which of the following correctly describes electrons as being standing waves?

- Standing waves propagate only through space
- Standing waves are fixed at one end
- Standing waves are fixed at both ends
- None of the above

2.

Which of the following describes the energy quantities involved in the electrons in different energy levels of an atom?

- Indistinct energy quantities
- Varying energy quantities
- Fixed energy quantities
- Both (a) and (b)

3.

Which of the following equations correctly represents the motion of one particle along the x-axis in space?

- [math]h^2/{4π^2m} {d^2psi}/{dx^2} + Vpsi = Epsi[/math]
- [math]-h^2/{4π^2m} {d^2psi}/{dx^2} + Vpsi = Epsi[/math]
- [math]h^2/{8π^2m} {d^2psi}/{dx^2} + Vpsi = Epsi[/math]
- [math]-h^2/{8π^2m} {d^2psi}/{dx^2} + Vpsi = Epsi[/math]

4.

Which of the following correctly describes one implication of the solution to Schrödinger's equation?

- Energy occurs in half-number multiples
- Energy always only contains one value
- Energy occurs in whole-number multiples
- Energy occurs in quarter-number multiples

5.

Which of the following is represented by [math]|psi^2|[/math]?

- Wave functions, also known as orbitals
- A probability distribution
- The energy of the particle
- (b) and (c)

6.

On an electron density map, how can one discern the most probable location of an electron?

- By the region that is most intense and darkest
- By the region that is light and dark
- By the region that is lightest
- None of the above

7.

Which of the following correctly represents a distinct feature of orbitals?

- They represent circular orbits
- They represent randomized regions of electrons
- They do not represent circular orbits, but rather probabilistic regions of electrons
- (a) and (b)

8.

Which of the following represents the simplified function involved in the Schrödinger Equation?

- [math]hat Hpsi=E/psi[/math]
- [math]hat Hpsi=Epsi[/math]
- [math]hat Hpsi^2=E/psi[/math]
- None of the above

9.

The Heisenberg Uncertainty Principle, which is used to determine uncertainties in position and in momentum, is significant for macroscopic objects.

- True
- False

10.

Name one limitation of wave functions and probability maps.

- Acceptable answers include the following:

• How an electron came to its present location

• When an electron will be in a particular location

• Where an electron will move towards

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