Q: If an electron has a de Broglie wavelength of $$1.2 \times 10$$^{-10}$$\ \mathrm{m}$$, what is its velocity? (Given: $$h = 6.626 \times 10$$^{-34}$$\ \mathrm{J\cdot s}$$, $$m_e = 9.11 \times 10$$^{-31}$$\ \mathrm{kg})$$

$$v = \dfrac{h}{m_e \lambda} = \dfrac{6.626 \times 10$$^{-34}$$}{9.11 \times 10$$^{-31}$$ \times 1.2 \times 10$$^{-10}$$} \approx 6.06 \times 10$$^{6}$$\ \mathrm{m/s}$$

Question 1

According to Bohr's model of the atom, what happens when an electron transitions from a higher energy orbit (n=3) to a lower energy orbit (n=2) in a hydrogen atom?

Accepted Answer

The atom emits a photon with energy equal to the difference between the two orbits.

Question 2

Which equation correctly represents the de Broglie wavelength of a particle?

Accepted Answer

$$\lambda = \dfrac{h}{mv}$$

Question 3

Why do we not observe wave properties for macroscopic objects like baseballs, even though the de Broglie relation applies to all matter?

Accepted Answer

Because the de Broglie wavelength of a baseball is so small compared to its size that it is insignificant.

Question 4

An electron in a hydrogen atom drops from $$n=4 to$$ $$n=2. $$Which of the following statements is true?

Accepted Answer

The electron emits a photon with energy equal to the difference in energy between $$n=4$$ and $$n=2.$$

Question 5

Which quantum number determines the shape of an atomic orbital?

Accepted Answer

Angular momentum quantum number, $$l$$

Question 6

For $$n=4$$, how many total orbitals are possible?

Accepted Answer

16

Question 7

Which set of quantum numbers is NOT allowed for an electron in an atom?

Accepted Answer

$$n=2,\ l=2,\ m_l=0,\ m_s=+\dfrac{1}{2}$$

Question 8

Which of the following best summarizes Heisenberg's uncertainty principle?

Accepted Answer

The more precisely the position of an electron is known, the less precisely its velocity can be known.

Question 9

How many $$d$$ orbitals are present in the $$n=5$$ principal energy level?

Accepted Answer

5

Question 10

Which quantum number specifies the orientation of an orbital in space?

Accepted Answer

Magnetic quantum number, $$m_l$$

Question 11

A beam of electrons is passed through two closely spaced slits and forms an interference pattern on a screen. What does this experiment demonstrate?

Accepted Answer

Electrons have wave-like properties.

Question 12

Which of the following is the correct set of possible values for $$l$$ when $$n=3$$?

Accepted Answer

0, 1, and 2

Question 13

If an electron has a de Broglie wavelength of $$1.2 	imes 10$$^{-10}$$\ \mathrm{m}$$, what is its velocity? (Given: $$h = 6.626 	imes 10$$^{-34}$$\ \mathrm{J\cdot s}$$, $$m_e = 9.11 	imes 10$$^{-31}$$\ \mathrm{kg})$$

Accepted Answer

$$v = \dfrac{h}{m_e \lambda} = \dfrac{6.626 	imes 10$$^{-34}$$}{9.11 	imes 10$$^{-31}$$ 	imes 1.2 	imes 10$$^{-10}$$} \approx 6.06 	imes 10$$^{6}$$\ \mathrm{m/s}$$

Question 14

Which of the following statements about atomic orbitals is correct?

Accepted Answer

$$d$$ orbitals are mainly shaped like a flat four-leaf clover.

Question 15

What is the total number of $$m_l$$ values possible for $$l=3$$?

Accepted Answer

7

Question 16

Which quantum number describes the orientation of the electron's spin?

Accepted Answer

Spin quantum number, $$m_s$$

Question 17

According to quantum mechanics, what is the best we can do to describe the location of an electron in an atom?

Accepted Answer

Describe the probability of finding it in a particular region.

Question 18

Which of the following statements about the principal quantum number $$n is $$FALSE?

Accepted Answer

As $$n$$ increases, the energy difference between levels increases.

Question 19

Which of the following best describes the concept of indeterminacy in electron behavior?

Accepted Answer

The path of an electron cannot be determined exactly; only probabilities can be assigned.

Atomic Structure: Bohr Model, Wave-Particle Duality, and Quantum Numbers

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