Question 1

Which experimental observation led to the development of the quantum theory of light?

Accepted Answer

The emission of electrons from a metal surface only when light of a certain minimum frequency shines on it.

Question 2

According to the photoelectric effect, what happens when light with a frequency below the threshold frequency shines on a metal surface?

Accepted Answer

No electrons are emitted, regardless of the light's intensity.

Question 3

Which equation correctly relates the energy of a photon to its frequency?

Accepted Answer

$E = h 
u$

Question 4

A metal has a work function (binding energy) $\phi$ of $2.0 	imes 10^{-19}$ J. What is the minimum frequency of light required to eject electrons from this metal? (Planck's constant $h = 6.626 	imes 10^{-34}$ J·s)

Accepted Answer

$3.02 	imes 10^{14}$ Hz

Question 5

Which statement best describes the emission spectrum of an element?

Accepted Answer

It consists of discrete lines of specific wavelengths unique to that element.

Question 6

According to de Broglie's hypothesis, what is the wavelength of an electron (mass $9.11 	imes 10^{-31}$ kg) moving at $2.65 	imes 10^6$ m/s? (Planck's constant $h = 6.626 	imes 10^{-34}$ J·s)

Accepted Answer

$2.74 	imes 10^{-10}$ m

Question 7

Which of the following best illustrates the concept of complementary properties in quantum mechanics?

Accepted Answer

Measuring the position of an electron more precisely increases the uncertainty in its momentum.

Question 8

Heisenberg's uncertainty principle can be mathematically expressed as:

Accepted Answer

$\Delta x \cdot \Delta v \geq \frac{h}{4\pi m}$

Question 9

Which quantum number determines the shape of an atomic orbital?

Accepted Answer

Angular momentum quantum number $l$

Question 10

How many orbitals are present in the $n = 3$ energy level of an atom?

Accepted Answer

9

Question 11

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

Accepted Answer

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

Question 12

What is the maximum number of electrons that can occupy the $n = 2$ principal energy level?

Accepted Answer

8

Question 13

Which of the following statements about atomic orbitals is correct?

Accepted Answer

A $p$ orbital has a dumbbell shape and there are three $p$ orbitals per energy level (for $n \geq 2$).

Question 14

If an electron in a hydrogen atom transitions from $n = 4$ to $n = 2$, what happens?

Accepted Answer

A photon is emitted with energy equal to the difference between the two energy levels.

Question 15

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

Accepted Answer

Magnetic quantum number $m_l$

Question 16

A sodium street lamp emits light at a wavelength of $589$ nm. What is the energy of one photon of this light? (Planck's constant $h = 6.626 	imes 10^{-34}$ J·s, speed of light $c = 3.00 	imes 10^8$ m/s)

Accepted Answer

$3.37 	imes 10^{-19}$ J

Question 17

Which of the following best explains why the emission spectrum of hydrogen contains only certain wavelengths?

Accepted Answer

Electrons in hydrogen can only occupy specific energy levels, so only certain energy transitions (and thus wavelengths) are possible.

Question 18

How many possible values of $m_l$ are there for $l = 2$?

Accepted Answer

5

Question 19

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

Accepted Answer

It determines the energy and size of the orbital.

Question 20

A hospital uses a photoelectric sensor to monitor patient heartbeats. If the sensor uses a metal with a threshold frequency of $5.0 	imes 10^{14}$ Hz, which color of visible light (red: $4.3 	imes 10^{14}$ Hz, green: $5.5 	imes 10^{14}$ Hz, blue: $6.7 	imes 10^{14}$ Hz) will cause electrons to be emitted?

Accepted Answer

Green and blue light only

8.2-8.5 The Quantum-Mechanical Model of the Atom: Wave-Particle Duality, Photoelectric Effect, and Atomic Structure

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