Q: According to the de Broglie hypothesis, what is the wavelength of an electron moving at 1.00% of the speed of light ($$c = 3.00 \times 10^8$\ \mathrm{m/s}$$, $$m_e = 9.11 \times 10$$^{-31}$$\ \mathrm{kg}$$)?

$$\lambda = \frac{h}{m_ev} = \frac{6.626 \times 10$$^{-34}$$\ \mathrm{J\cdot s}}{9.11 \times 10$$^{-31}$$\ \mathrm{kg} \times 3.00 \times 10^6$\ \mathrm{m/s}} \approx 2.43 \times 10$$^{-10}$$\ \mathrm{m}$$

Q: A baseball (mass $$0.145\ \mathrm{kg}) is $$thrown at $$105\ \mathrm{mph}$$ ($$47.0\ \mathrm{m/s}). $$What is its de Broglie wavelength?

$$\lambda = \frac{6.626 \times 10$$^{-34}$$}{0.145 \times 47.0} \approx 9.7 \times 10$$^{-35}$$\ \mathrm{m}$$

Q: If an electron in a hydrogen atom transitions from $$n=3 to$$ $$n=1$$, what is the energy change ($$\Delta E) $$associated with this transition? (Use $$E_n = -2.18 \times 10$$^{-18}$$\ \mathrm{J} \times \frac{1}{n^2$})$$

$$\Delta E = E_1$ - E_3$ = -2.18 \times 10$$^{-18}$$ \left(1 - \frac{1}{9}\right) = -1.94 \times 10$$^{-18}$$\ \mathrm{J}$$

Question 1

Which of the following best describes the result of the double-slit experiment with electrons, as shown in the provided diagrams?

Accepted Answer

Electrons exhibit both wave and particle behavior, producing an interference pattern on the detector.

Question 2

According to the de Broglie hypothesis, what is the wavelength of an electron moving at 1.00% of the speed of light ($$c = 3.00 	imes 10^8$\ \mathrm{m/s}$$, $$m_e = 9.11 	imes 10$$^{-31}$$\ \mathrm{kg}$$)?

Accepted Answer

$$\lambda = \frac{h}{m_ev} = \frac{6.626 	imes 10$$^{-34}$$\ \mathrm{J\cdot s}}{9.11 	imes 10$$^{-31}$$\ \mathrm{kg} 	imes 3.00 	imes 10^6$\ \mathrm{m/s}} \approx 2.43 	imes 10$$^{-10}$$\ \mathrm{m}$$

Question 3

Which of the following sets of quantum numbers is NOT allowed for an electron in an atom?

Accepted Answer

$$n=3,\ l=1,\ m_l=+2$$

Question 4

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

Accepted Answer

25

Question 5

Which quantum number determines the shape of an atomic orbital?

Accepted Answer

Angular momentum quantum number ($$l)$$

Question 6

A baseball (mass $$0.145\ \mathrm{kg}) is $$thrown at $$105\ \mathrm{mph}$$ ($$47.0\ \mathrm{m/s}). $$What is its de Broglie wavelength?

Accepted Answer

$$\lambda = \frac{6.626 	imes 10$$^{-34}$$}{0.145 	imes 47.0} \approx 9.7 	imes 10$$^{-35}$$\ \mathrm{m}$$

Question 7

Which statement best explains why macroscopic objects like baseballs do not exhibit observable quantum interference patterns?

Accepted Answer

Their de Broglie wavelengths are much too small to produce observable interference effects.

Question 8

In the context of quantum numbers, what is the maximum number of electrons that can occupy the $$n=3$$ shell?

Accepted Answer

18

Question 9

Which of the following best describes the difference between the interference pattern produced by bullets and that produced by electrons in a double-slit experiment?

Accepted Answer

Electrons produce an interference pattern due to their wave-like nature, while bullets produce two bands corresponding to the slits.

Question 10

For the quantum numbers $$n=5$$, $$l=3$$, $$m_l=-2$$, which subshell and orbital is specified?

Accepted Answer

5f, one of the seven possible f orbitals

Question 11

Which quantum number(s) determine the number of orbitals in a given subshell?

Accepted Answer

The magnetic quantum number ($$m_l$$), which ranges from $$-l to$$ $$+l$$

Question 12

What is the total number of possible values for the magnetic quantum number $$m_l$$ when $$l=2$$?

Accepted Answer

5

Question 13

Which of the following best explains the observation of an interference pattern when large molecules such as $$C_{60} ($$buckyballs) are sent through a double-slit apparatus?

Accepted Answer

Large molecules like $$C_{60}$$ exhibit wave-like properties and can interfere with themselves, producing an interference pattern.

Question 14

If an electron in a hydrogen atom transitions from $$n=3 to$$ $$n=1$$, what is the energy change ($$\Delta E) $$associated with this transition? (Use $$E_n = -2.18 	imes 10$$^{-18}$$\ \mathrm{J} 	imes \frac{1}{n^2$})$$

Accepted Answer

$$\Delta E = E_1$ - E_3$ = -2.18 	imes 10$$^{-18}$$ \left(1 - \frac{1}{9}ight) = -1.94 	imes 10$$^{-18}$$\ \mathrm{J}$$

Question 15

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

Accepted Answer

It determines the overall energy and size of the orbital.

Question 16

What is the maximum number of electrons that can occupy the $$4d$$ subshell?

Accepted Answer

10

Question 17

Which of the following best describes the effect of observing which slit an electron passes through in a double-slit experiment?

Accepted Answer

The interference pattern disappears and a particle-like pattern is observed.

Question 18

For $$l=3$$, how many possible values of $$m_l$$ are there, and what type of orbital does this correspond to?

Accepted Answer

7 possible values; f orbital

Question 19

Which of the following quantum numbers is responsible for distinguishing between different orientations of the same type of orbital?

Accepted Answer

Magnetic quantum number ($$m_l)$$

Quantum Behavior and Quantum Numbers: Study Notes

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