Q: According to the de Broglie hypothesis, what is the wavelength $\lambda$ of an electron moving at 1.00% of the speed of light ($c = 3.00 \times 10^8$ m/s)? (Electron mass $m_e = 9.11 \times 10^{-31}$ kg, $h = 6.626 \times 10^{-34}$ J·s)

$\lambda = 7.27 \times 10^{-11}$ m

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 characteristic of waves.

Question 2

According to the de Broglie hypothesis, what is the wavelength $\lambda$ of an electron moving at 1.00% of the speed of light ($c = 3.00 	imes 10^8$ m/s)? (Electron mass $m_e = 9.11 	imes 10^{-31}$ kg, $h = 6.626 	imes 10^{-34}$ J·s)

Accepted Answer

$\lambda = 7.27 	imes 10^{-11}$ m

Question 3

Which of the following statements about the interference experiment with bullets, water waves, and electrons is correct?

Accepted Answer

Water waves and electrons both produce interference patterns, but bullets do not.

Question 4

Given the quantum numbers $n = 4$, $l = 4$, $m = 0$, which statement is correct?

Accepted Answer

The value of $l$ cannot be equal to $n$; it must be less than $n$.

Question 5

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

Accepted Answer

50

Question 6

Which quantum numbers describe a 3d orbital?

Accepted Answer

$n = 3$, $l = 2$, $m = -2$

Question 7

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

Accepted Answer

$9.80 	imes 10^{-34}$ m

Question 8

Which of the following sets of quantum numbers is NOT allowed?

Accepted Answer

$n = 3$, $l = 3$, $m = +2$

Question 9

What is the physical significance of the principal quantum number $n$ in the hydrogen atom?

Accepted Answer

It determines the overall energy and size of the orbital.

Question 10

For a given value of $l = 2$, how many possible values of $m$ are there?

Accepted Answer

5

Question 11

Which experiment demonstrates the wave-particle duality of matter most directly?

Accepted Answer

The double-slit experiment with electrons

Question 12

If an electron in a hydrogen atom transitions from $n = 3$ to $n = 2$, what happens?

Accepted Answer

The electron emits energy as a photon.

Question 13

Which quantum number determines the number of nodal planes in an orbital?

Accepted Answer

Azimuthal (angular momentum) quantum number $l$

Question 14

A hydrogen atom has an electron in the $n = 2$, $l = 1$, $m = 0$ state. What is the shape and orientation of this orbital?

Accepted Answer

Dumbbell-shaped, oriented along the $z$-axis

Question 15

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

Accepted Answer

Their de Broglie wavelengths are too small to be detected.

Question 16

What is the total number of orbitals in the $n = 4$ shell?

Accepted Answer

16

Question 17

Which quantum number(s) determine the energy of an electron in a hydrogen atom?

Accepted Answer

Only $n$

Question 18

If a measurement is made to determine through which slit an electron passes in a double-slit experiment, what is the result?

Accepted Answer

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

Question 19

Which of the following statements about the magnetic quantum number $m$ is correct?

Accepted Answer

$m$ determines the orientation of the orbital in space.

Question 20

For $n = 3$, what is the maximum value of $l$ and how many $d$ orbitals are there?

Accepted Answer

Maximum $l = 2$; 5 $d$ orbitals

Quantum Behavior and Models in General Chemistry

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