Question 1

Which of the following statements is(are) true? 
I. An excited atom can return to its ground state by absorbing electromagnetic radiation.
II. The energy of an atom is increased when electromagnetic radiation is emitted from it.
III. The energy of electromagnetic radiation increases as its frequency increases.
IV. An electron in the n = 4 state in the hydrogen atom can go to the n = 2 state by emitting electromagnetic radiation at the appropriate frequency.
V. The frequency and wavelength of electromagnetic radiation are inversely proportional to each other.
A) III, V
B) II, III, IV
C) I, II, IV
D) I, II, III
E) III, IV, V

Accepted Answer

III is true because the energy of electromagnetic radiation is directly proportional to its frequency. IV is true because an electron can transition to a lower energy state by emitting radiation. V is true because frequency and wavelength are inversely proportional.

Question 2

From the following list of observations, choose the one that most clearly supports the conclusion that electrons in atoms have quantized energies.
A) the photoelectric effect
B) the scattering of alpha particles by metal foil
C) diffraction
D) cathode "rays"
E) the emission spectrum of hydrogen

Accepted Answer

The emission spectrum of hydrogen shows that the energy emitted by hydrogen atoms is quantized and occurs in discrete wavelengths, providing evidence for the quantized energy levels of electrons in atoms.

Question 3

Which of the following frequencies corresponds to light with the longest wavelength? A) 9.12 *10¹² s^-¹ B) 3.20 * 10⁹ s^-¹ C) 8.50 * 10²⁰ s^-¹ D) 3.00 *10¹³ s^-¹ E) 4.12 * 10⁵ s^-¹

Accepted Answer

The wavelength of light is inversely proportional to its frequency. Therefore, the light with the lowest frequency will have the longest wavelength. Among the given options, 4.12 × 10⁵ s^-1 is the lowest frequency.

Question 4

From the following list of observations, choose the one that most clearly supports the conclusion of de Broglie wavelengths.
A) cathode "rays"
B) the scattering of alpha particles by metal foil
C) diffraction
D) the emission spectrum of hydrogen
E) the photoelectric effect

Accepted Answer

Diffraction is the phenomenon where waves bend around obstacles or spread through gaps. It was observed with light, but also with electrons and other particles. The diffraction pattern is similar to that of waves, and can be explained by wave interference. The fact that particles, like electrons, can display wave-like behavior supports the idea that they have a wavelength, as proposed by de Broglie.

Question 5

In Bohr's atomic theory, when an electron moves from one energy level to another energy level more distant from the nucleus,
A) energy is emitted.
B) energy is absorbed.
C) light is emitted.
D) no change in energy occurs.
E) none of these

Accepted Answer

When an electron moves from one energy level to another energy level that is farther from the nucleus, it requires energy and is therefore absorbed. This energy can be provided by heating the atom or by electromagnetic radiation such as ultraviolet light.

Question 6

Light has a wavelength of 5.8 *10² nm. What is the energy of a photon of this light? A) 2.62 *10¹⁸ J B) 3.81 * 10^-²⁰ J C) 1.28 * 10^-¹⁸ J D) 1.14 *10^-¹⁹ J E) 3.42 * 10^-¹⁹ J

Accepted Answer

The energy of a photon can be calculated using the formula E = hc/λ, where h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength in meters. Converting 5.8 x 10^2 nm to meters gives 5.8 x 10^-7 m. Substituting these values into the formula gives E ≈ 3.42 x 10^-19 J.

Question 7

Consider an atom traveling at 1% of the speed of light. The de Broglie wavelength is found to be 3.31 *10^-³ pm. Which element is this? A) P B) Ca C) He D) F E) Be

Accepted Answer

The de Broglie wavelength formula is λ = h / (mv), where h is Planck's constant, m is mass, and v is velocity. Given the wavelength and velocity, we can solve for mass and identify the element. The calculated mass corresponds to calcium (Ca).

Question 8

Which form of electromagnetic radiation has the shortest wavelengths?
A) gamma rays
B) X rays
C) radio waves
D) microwaves
E) infrared radiation

Accepted Answer

Gamma rays have the shortest wavelengths of all forms of electromagnetic radiation. They have wavelengths ranging from 10^-12 to 10^-16 meters, which is shorter than X-rays, ultraviolet radiation, visible light, infrared radiation, microwaves, and radio waves.

Question 9

From the following list of observations, choose the one that most clearly supports the conclusion that atoms contain electrons.
A) the emission spectrum of hydrogen
B) cathode "rays"
C) diffraction
D) the photoelectric effect
E) the scattering of alpha particles by metal foil

Accepted Answer

The observation of cathode "rays" (also known as electron beams) demonstrates the existence of negatively charged particles within atoms.

Question 10

From the following list of observations, choose the one that most clearly supports the conclusion that electrons have wave properties.
A) the scattering of alpha particles by metal foil
B) the photoelectric effect
C) the emission spectrum of hydrogen
D) diffraction
E) cathode "rays"

Accepted Answer

Diffraction is a phenomenon in which waves bend and spread out when passing through a narrow opening or around an obstacle. Electrons have been observed to exhibit diffraction when passing through a series of closely spaced slits, indicating that they have wave-like properties.

Question 11

A photographic film needs a minimum of 80.0 kJ/mol for exposure. What is the longest wavelength of radiation with sufficient energy to expose the film? A) 1.50 * 10^-³ m B) 1.50 *10^-¹² m C) 1.50 * 10^-⁶ m D) 1.50 * 10^-⁹ m E) none of these

Accepted Answer

The answer of A photographic film needs a minimum of...

Question 12

What is the wavelength of light that is emitted when an excited electron in the hydrogen atom falls from the n = 5 level to the n = 2 level? A) 5.82 *10^-⁷ m B) 6.50 * 10^-⁷ m C) 4.34 *10^-⁷ m D) 5.12*10^-⁷ m E) none of these

Accepted Answer

The wavelength of light emitted during the transition from the n=5 to the n=2 level in hydrogen can be calculated using the Rydberg formula: 
1/λ = R(1/nf^2 - 1/ni^2)
where R is the Rydberg constant, nf is the final energy level (n=2), and ni is the initial energy level (n=5). Plugging in the values: 
1/λ = R(1/2^2 - 1/5^2)
1/λ = R(9/100 - 4/25)
1/λ = R(1/100)
λ = 100R = 100(1.0968 x 10^7 m^-1) = 1.0968 x 10^9 m^-1 = 4.34 x 10^-7 m or 434 nm. 
Therefore, the correct answer is choice C.

Question 13

What is the wavelength, in nanometers, of a photon of light whose frequency is 5.38 *10¹⁴ Hz? A) 1.19 * 10^-⁷ nm B) 2.71 * 10² nm C) 5.58 * 10² nm D) 1.79 * 10² nm E) 3.69 * 10² nm

Accepted Answer

We can use the formula c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency.
We first need to convert the frequency from Hz to s^-1:
5.38 x 10^14 Hz = 5.38 x 10^14 s^-1
Then we can plug in the values to solve for λ:
c = λν
λ = c/ν
λ = (3.00 x 10^8 m/s) / (5.38 x 10^14 s^-1)
λ = 5.58 x 10^-7 m or 558 nm
However, the answer choices are given in nanometers, so we need to convert:
558 nm = 5.58 x 10^1 nm
Therefore, the answer is choice C: 5.58 x 10^1 nm.

Question 14

Consider the following portion of the energy-level diagram for hydrogen: 
-For which of the following transitions does the light emitted have the longest wavelength?
A) n = 2 to n = 1
B) n = 4 to n = 1
C) n = 3 to n = 2
D) n = 4 to n = 2
E) n = 4 to n = 3

Accepted Answer

The wavelength of the light emitted during an electronic transition in an atom is inversely proportional to the energy change associated with the transition. The energy change is smallest when the transition occurs between adjacent energy levels, such as from n = 4 to n = 3, resulting in the longest wavelength of light emitted.

Question 15

In general, Z is less than Z_eff.

Accepted Answer

As per the given inequality, Z is greater than or equal to Z_eff. Therefore, the statement "Z is less than Z_eff" is false.

Question 16

A photographic film needs a minimum of 80.0 kJ/mol for exposure. The frequencies of visible light are in the range 7.5 * 10¹⁴ Hz to 4.3 * 10¹⁴ Hz. Is the radiation visible to the human eye? A) yes B) no C) More information is needed.

Accepted Answer

The answer of A photographic film needs a minimum of...

Question 17

From the following list of observations, choose the one that most clearly supports the conclusion that the mass of the atom is located mainly in the nucleus.
A) the emission spectrum of hydrogen
B) the photoelectric effect
C) diffraction
D) the scattering of alpha particles by metal foil
E) cathode "rays"

Accepted Answer

The scattering of alpha particles by metal foil was the experiment conducted by Rutherford which indicated that the mass of the atom is concentrated in a small, dense positively-charged region within the atom, which he called the nucleus.

Question 18

Which of the following is a reasonable criticism of the Bohr model of the atom?
A) It shows the electrons to exist outside of the nucleus.
B) It does not adequately predict the ionization energy of the first-energy-level electrons for elements other than hydrogen.
C) It makes no attempt to explain why the negative electron does not eventually fall into the positive nucleus.
D) It does not adequately predict the ionization energy of the valence electron(s) for elements other than hydrogen.
E) It does not adequately predict the line spectrum of hydrogen.

Accepted Answer

The Bohr model is only accurate for a single electron system like hydrogen. For elements with multiple electrons, the model fails to predict the ionization energy of the valence electrons.

Question 19

In an investigation of the electronic absorption spectrum of a particular element, it is found that a photon having $\lambda$ = 500 nm provides just enough energy to promote an electron from the second quantum level to the third. From this information, we can deduce
A) the energy of the n = 2 level.
B) the sum of the energies of the n = 2 and n = 3 levels.
C) the difference between the energies of the n = 2 and n = 3 levels.
D) the energy of the n = 3 level.
E) all of these.

Accepted Answer

By using the formula E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is wavelength, we can find the energy of the photon with wavelength 500 nm. Then, we can calculate the energy difference between the n = 2 and n = 3 levels by using the formula ΔE = E_final - E_initial = E_3 - E_2, where ΔE is the energy difference, and E_final and E_initial are the energies of the final and initial states, respectively. Therefore, we can deduce the energy difference between the n = 2 and n = 3 levels, which is choice C. We cannot determine the individual energies of either level, so choices A and D are incorrect. We also cannot calculate the sum of the energies of the n = 2 and n = 3 levels, so choice B is incorrect. Therefore, the best choice is C.

Question 20

From the following list of observations, choose the one that most clearly supports the conclusion that electromagnetic radiation has wave characteristics.
A) diffraction
B) the emission spectrum of hydrogen
C) the scattering of alpha particles by metal foil
D) cathode "rays"
E) the photoelectric effect

Accepted Answer

Diffraction is the bending of waves around obstacles or through openings, which is a clear indication of wave-like behavior.

Quiz 12: Quantum Mechanics and Atomic Theory

From the following list of observations, choose the one that most clearly supports the conclusion that electrons in atoms have quantized energies.

Which of the following frequencies corresponds to light with the longest wavelength?

From the following list of observations, choose the one that most clearly supports the conclusion of de Broglie wavelengths.

In Bohr's atomic theory, when an electron moves from one energy level to another energy level more distant from the nucleus,

Light has a wavelength of 5.8 *102 nm. What is the energy of a photon of this light?

Consider an atom traveling at 1% of the speed of light. The de Broglie wavelength is found to be 3.31 *10-3 pm. Which element is this?

Which form of electromagnetic radiation has the shortest wavelengths?

From the following list of observations, choose the one that most clearly supports the conclusion that atoms contain electrons.

From the following list of observations, choose the one that most clearly supports the conclusion that electrons have wave properties.

A photographic film needs a minimum of 80.0 kJ/mol for exposure. What is the longest wavelength of radiation with sufficient energy to expose the film?

What is the wavelength of light that is emitted when an excited electron in the hydrogen atom falls from the n = 5 level to the n = 2 level?

What is the wavelength, in nanometers, of a photon of light whose frequency is 5.38 *1014 Hz?

Consider the following portion of the energy-level diagram for hydrogen: -For which of the following transitions does the light emitted have the longest wavelength?

In general, Z is less than Zeff.

A photographic film needs a minimum of 80.0 kJ/mol for exposure. The frequencies of visible light are in the range 7.5 * 1014 Hz to 4.3 * 1014 Hz. Is the radiation visible to the human eye?

From the following list of observations, choose the one that most clearly supports the conclusion that the mass of the atom is located mainly in the nucleus.

Which of the following is a reasonable criticism of the Bohr model of the atom?

In an investigation of the electronic absorption spectrum of a particular element, it is found that a photon having λ\lambdaλ = 500 nm provides just enough energy to promote an electron from the second quantum level to the third. From this information, we can deduce

From the following list of observations, choose the one that most clearly supports the conclusion that electromagnetic radiation has wave characteristics.

Light has a wavelength of 5.8 *10² nm. What is the energy of a photon of this light?

Consider an atom traveling at 1% of the speed of light. The de Broglie wavelength is found to be 3.31 *10^-³ pm. Which element is this?

What is the wavelength, in nanometers, of a photon of light whose frequency is 5.38 *10¹⁴ Hz?

In general, Z is less than Z_eff.

A photographic film needs a minimum of 80.0 kJ/mol for exposure. The frequencies of visible light are in the range 7.5 * 10¹⁴ Hz to 4.3 * 10¹⁴ Hz. Is the radiation visible to the human eye?

In an investigation of the electronic absorption spectrum of a particular element, it is found that a photon having $\lambda$ = 500 nm provides just enough energy to promote an electron from the second quantum level to the third. From this information, we can deduce