Q: What is the de Broglie wavelength of an electron moving at $2.45 \times 10^6$ m/s? ($m_e = 9.11 \times 10^{-31}$ kg, $h = 6.626 \times 10^{-34}$ J·s)

$\lambda = 2.97 \times 10^{-10}$ m

Question 1

Which statement best explains why electrons in atoms cannot be directly observed without altering their behavior?

Accepted Answer

Electrons are so small that any attempt to observe them, such as shining light, changes their energy and position.

Question 2

Which property of light determines its color?

Accepted Answer

Frequency

Question 3

A green laser and a dim green laser emit light of the same frequency. What is the difference between them?

Accepted Answer

The bright green laser has a greater amplitude than the dim green laser.

Question 4

Which equation correctly relates the speed of light ($c$), wavelength ($\lambda$), and frequency ($
u$)?

Accepted Answer

$c = \lambda 
u$

Question 5

A laser emits light with a wavelength of 515 nm. What is the frequency of this light? (Speed of light $c = 3.00 	imes 10^8$ m/s)

Accepted Answer

$
u = 5.83 	imes 10^{14}$ Hz

Question 6

Which type of electromagnetic radiation has the highest energy per photon?

Accepted Answer

Gamma rays

Question 7

What phenomenon occurs when light waves bend around an obstacle or opening that is about the same size as their wavelength?

Accepted Answer

Diffraction

Question 8

According to Einstein's explanation of the photoelectric effect, what determines whether electrons are ejected from a metal surface?

Accepted Answer

The frequency of the incident light must be above a threshold value.

Question 9

Calculate the energy of a single photon of light with a wavelength of 525 nm. ($h = 6.626 	imes 10^{-34}$ J·s, $c = 3.00 	imes 10^8$ m/s)

Accepted Answer

$E = 3.79 	imes 10^{-19}$ J

Question 10

Which statement best summarizes the Heisenberg uncertainty principle?

Accepted Answer

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

Question 11

Which quantum number determines the shape of an atomic orbital?

Accepted Answer

Angular momentum quantum number ($l$)

Question 12

How many d orbitals exist in a principal energy level where $l = 2$?

Accepted Answer

5

Question 13

Which transition in a hydrogen atom emits light with the shortest wavelength?

Accepted Answer

$n=5$ to $n=4$

Question 14

What is the de Broglie wavelength of an electron moving at $2.45 	imes 10^6$ m/s? ($m_e = 9.11 	imes 10^{-31}$ kg, $h = 6.626 	imes 10^{-34}$ J·s)

Accepted Answer

$\lambda = 2.97 	imes 10^{-10}$ m

Question 15

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

Accepted Answer

Magnetic quantum number ($m_l$)

Question 16

A metal surface ejects electrons when struck by yellow light. What will happen if the surface is struck with ultraviolet light?

Accepted Answer

Electrons will be ejected, and they will have greater kinetic energy than those ejected by yellow light.

Question 17

Which of the following best describes the difference between constructive and destructive interference?

Accepted Answer

Constructive interference occurs when waves are in phase and add to make a larger wave; destructive interference occurs when waves are out of phase and cancel each other.

Question 18

Which quantum number can have values of $+\frac{1}{2}$ or $-\frac{1}{2}$?

Accepted Answer

Spin quantum number ($m_s$)

Question 19

Which statement explains why macroscopic objects like baseballs do not exhibit observable wave properties?

Accepted Answer

Because of the baseball's large mass, its de Broglie wavelength is minuscule and insignificant compared to its size.

Quantum-Mechanical Model of the Atom: Structure, Properties, and Light

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