Question 1

Excited hydrogen atoms radiate energy in the

Accepted Answer

Excited hydrogen atoms can emit radiation in the infrared, visible, and ultraviolet regions as they transition to lower energy levels, covering a broad spectrum of electromagnetic radiation.

Question 2

In the photoelectric effect, a photon with an energy of 5.3 × 10⁻¹⁹ J strikes an electron in a metal. Of this energy, 3.6 × 10⁻¹⁹ J is the minimum energy required for the electron to escape from the metal. The remaining energy appears as kinetic energy of the photoelectron. What is the velocity of the photoelectron, assuming it was initially at rest?

Accepted Answer

The kinetic energy of the photoelectron can be found by subtracting the minimum energy required for the electron to escape from the total energy of the photon:
$KE = E_{photon} - E_{min} = (5.3 	imes 10^{-19} J) - (3.6 	imes 10^{-19} J) = 1.7 	imes 10^{-19} J$

We can then use the kinetic energy formula to find the velocity of the photoelectron:
$KE = \frac{1}{2}mv^2$
$1.7 	imes 10^{-19} J = \frac{1}{2}(9.11 	imes 10^{-31} kg)v^2$
$v = \sqrt{\frac{2(1.7 	imes 10^{-19} J)}{9.11 	imes 10^{-31} kg}}$
$v = 6.1 	imes 10^5 m/s = 6.1 	imes 10^{14} nm/s$

Therefore, the best choice is D.

Question 3

Platinum, which is widely used as a catalyst, has a work functionΦ (the minimum energy needed to eject an electron from the metal surface) of 9.05 × 10⁻¹⁹ J. What is the longest wavelength of light which will cause electrons to be emitted?

Accepted Answer

The longest wavelength of light that can cause electron emission is calculated using the equation λ = hc/Φ, where h is Planck's constant and c is the speed of light. Substituting the given work function, the longest wavelength is approximately 2.196 × 10⁻⁷ m.

Question 4

The size of an atomic orbital is associated with

Accepted Answer

The size of an atomic orbital is associated with the principal quantum number (n). As the value of n increases, the size of the orbitals also increases.

Question 5

The Bohr theory of the hydrogen atom predicts the energy difference (in J) between the n = 3 and the n = 5 state to be

Accepted Answer

The energy difference between two energy levels in the hydrogen atom is given by the formula:
ΔE = -Rh[(1/nf^2) - (1/ni^2)]
where Rh is the Rydberg constant, nf and ni are the final and initial energy levels, respectively.
For this problem, we have:
ΔE = -Rh[(1/5^2) - (1/3^2)]
Substituting the values of Rh and simplifying, we get:
ΔE = 1.55 × 10^-19 J

Question 6

Use the Rydberg equation to calculate the frequency of a photon absorbed when the hydrogen atom undergoes a transition from n₁ = 2 to n₂ = 4. (R = 1.096776 × 10⁷ m⁻¹)

Accepted Answer

The Rydberg equation for frequency is given by ν = R * c * (1/n1² - 1/n2²). Substituting the given values, ν = 1.096776 × 10⁷ m⁻¹ * 3 × 10⁸ m/s * (1/2² - 1/4²) = 6.165 × 10¹⁴ s⁻¹.

Question 7

The de Broglie equation predicts that the wavelength (in m) of a proton moving at 1000. m/s is

Accepted Answer

The de Broglie wavelength is calculated using the formula λ = h/p, where h is Planck's constant (6.626 × 10^-34 m^2 kg/s) and p is the momentum (mass × velocity). For a proton (mass ≈ 1.67 × 10^-27 kg) moving at 1000 m/s, the wavelength is approximately 3.96 × 10^-10 m.

Question 8

According to the Rydberg equation, the line with the shortest wavelength in the emission spectrum of atomic hydrogen is predicted to lie at a wavelength (in nm) of

Accepted Answer

The Rydberg equation predicts that the shortest wavelength (highest energy) transition in the hydrogen spectrum occurs as n approaches infinity to n=1, which corresponds to the Lyman series limit at 91.2 nm.

Question 9

The ionization energy is the energy needed to remove an electron from an atom. In the Bohr model of the hydrogen atom, this means exciting the electron to the n = ∞ state. What is the ionization energy in kJ/mol, for hydrogen atoms initially in the n = 2 energy level?

Accepted Answer

The ionization energy from the n = 2 level can be calculated using the Rydberg formula for the energy difference between levels in the hydrogen atom, which is given by $E = R_H \left( \frac{1}{n^2_{\text{initial}}} - \frac{1}{n^2_{\text{final}}} \right)$, where $R_H$ is the Rydberg constant (approximately $2.18 \times 10^{-18}$ J). For ionization, $n_{\text{final}} = \infty$ (which makes the second term zero) and $n_{\text{initial}} = 2$. Plugging these values in gives $E = 2.18 \times 10^{-18} J \times \left( \frac{1}{2^2} - 0 \right) = 5.45 \times 10^{-19} J$. To convert this energy to kJ/mol, we use Avogadro's number ($6.022 \times 10^{23} \text{mol}^{-1}$): $5.45 \times 10^{-19} J \times 6.022 \times 10^{23} \text{mol}^{-1} = 3.28 \times 10^5 J/mol = 328 kJ/mol$.

Question 10

A sprinter must average 24.0 mi/h to win a 100-m dash in 9.30 s. What is his wavelength at this speed if his mass is 84.5 kg?

Accepted Answer

We can use the formula λ = h/mv, where h is Planck's constant, m is the mass of the object in motion, v is the velocity, and λ is the wavelength. 
First, we need to convert the speed to m/s: 
24.0 mi/h = (24.0 mi/h)(1.609344 km/mi)(1000 m/km)(1 h/3600 s) = 10.67 m/s
Now we can solve for the wavelength: 
λ = (6.626 x 10^-34 J*s)/(84.5 kg)(10.67 m/s) = 7.29 x 10^-9 m = 7.29 nm 
Therefore, the answer is choice A.

Question 11

Consider the following adjectives used to describe types of spectrum: continuous, line, atomic, emission and absorption.How many of them are appropriate to describe the spectrum of radiation given off by a black body?

Accepted Answer

The spectrum of radiation given off by a black body can be described as continuous and emission. A continuous spectrum is produced by a source that emits radiation over a wide range of wavelengths, while an emission spectrum is produced by a gas that emits radiation at specific wavelengths. Black bodies emit radiation over a wide range of wavelengths, so a continuous spectrum is appropriate. Additionally, as the black body heats up, it emits more and more radiation at specific wavelengths, creating an emission spectrum. Therefore, both continuous and emission spectra are appropriate to describe the spectrum of radiation given off by a black body.

Question 12

According to the Rydberg equation, the longest wavelength (in nm) in the series of H-atom lines with n₁ = 3 is

Accepted Answer

The Rydberg equation for the wavelength ($\lambda$) of light emitted when an electron transitions between energy levels in a hydrogen atom is given by $\frac{1}{\lambda} = R_H \left( \frac{1}{n_{\text{lower}}^2} - \frac{1}{n_{\text{upper}}^2} \right)$, where $R_H$ is the Rydberg constant ($1.097 \times 10^7 \text{ m}^{-1}$), $n_{\text{lower}}$ is the principal quantum number of the lower energy level, and $n_{\text{upper}}$ is the principal quantum number of the higher energy level. For the longest wavelength, we want the smallest energy difference, which occurs for a transition from $n = 4$ to $n = 3$. Plugging these values into the Rydberg formula and solving for $\lambda$ gives the longest wavelength in the series. Calculating this yields a wavelength of approximately 1875 nm, making option A correct.

Question 13

Line spectra from all regions of the electromagnetic spectrum, including the Paschen series of infrared lines for hydrogen, are used by astronomers to identify elements present in the atmospheres of stars. Calculate the wavelength of the photon emitted when the hydrogen atom undergoes a transition from n = 5 to n = 3. (R = 1.096776 × 10⁷ m⁻¹)

Accepted Answer

The wavelength of the photon emitted during the transition from n = 5 to n = 3 in hydrogen can be calculated using the Rydberg formula for hydrogen: 1/λ = R(1/n1² - 1/n2²). Substituting n1 = 3, n2 = 5, and R = 1.096776 × 10⁷ m⁻¹, we find λ ≈ 1282 nm.

Question 14

What type of spectrum, if any, would be produced if the light radiated by a heated atomic gas were to be dispersed through a prism?

Accepted Answer

Dispersing the light radiated by a heated atomic gas through a prism would produce a spectrum of discrete lines of different colors, known as an emission line spectrum. These lines correspond to specific wavelengths of light emitted by the electrons in the atoms as they transition between energy levels.

Question 15

An electron in the n = 6 level emits a photon with a wavelength of 410.2 nm. To what energy level does the electron move?

Accepted Answer

The energy difference between two levels in the hydrogen atom is given by the formula derived from the Rydberg equation: $\Delta E = E_f - E_i = R_H \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right)$, where $R_H$ is the Rydberg constant, $n_i$ is the initial energy level, and $n_f$ is the final energy level. The wavelength of the emitted photon is related to the energy difference by the equation $E = \frac{hc}{\lambda}$, where $h$ is Planck's constant, $c$ is the speed of light, and $\lambda$ is the wavelength. Given the wavelength, we can calculate the energy of the emitted photon and then use the Rydberg formula to find the final energy level. The given wavelength corresponds to a transition to the $n = 2$ level for a photon emitted in the Balmer series of the hydrogen spectrum.

Question 16

For all the allowed vibration(s) (wavelength(s)) of a plucked guitar string, what is the correct relationship between the length of the string, L, and the wavelength, λ?

Accepted Answer

The correct relationship for the allowed vibrations of a plucked guitar string is L = nλ/2, where n is a positive integer. This formula represents the fundamental frequency and its harmonics, with n=1 being the fundamental frequency, n=2 the first overtone, and so on. This relationship arises because the string supports standing waves that have nodes at both ends, and the length of the string is equal to an integer multiple of half wavelengths.

Question 17

According to the Heisenberg uncertainty principle, if the uncertainty in the speed of an electron is 3.5 × 10³ m/s, the uncertainty in its position (in m) is at least

Accepted Answer

The Heisenberg uncertainty principle states that Δx * Δp ≥ ħ/2, where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and ħ is the reduced Planck's constant (approximately 1.0545718 × 10^-34 Js). Given the uncertainty in speed (Δv) is 3.5 × 10^3 m/s, and using the electron's mass (9.10938356 × 10^-31 kg), we can calculate Δp = m * Δv. Solving for Δx gives approximately 1.7 × 10^-8 m.

Question 18

For potassium metal, the work functionΦ (the minimum energy needed to eject an electron from the metal surface) is 3.68 × 10⁻¹⁹ J. Which is the longest wavelength of the following which could excite photoelectrons?

Accepted Answer

The answer of For potassium metal, the work functionΦ (the...

Question 19

Consider the following adjectives used to describe types of spectrum: continuous, line, atomic, emission and absorption.How many of them are appropriate to describe the spectrum of radiation absorbed by a sample of mercury vapor?

Accepted Answer

Atomic, emission, and absorption are appropriate to describe the spectrum of radiation absorbed by a sample of mercury vapor.

Question 20

According to the Bohr theory of the hydrogen atom, the minimum energy (in J) needed to ionize a hydrogen atom from the n = 2 state is

Accepted Answer

The answer of According to the Bohr theory of the...

Quiz 7: Quantum Theory and Atomic Structure

Excited hydrogen atoms radiate energy in the

Platinum, which is widely used as a catalyst, has a work functionΦ (the minimum energy needed to eject an electron from the metal surface) of 9.05 × 10⁻¹⁹ J. What is the longest wavelength of light which will cause electrons to be emitted?

The size of an atomic orbital is associated with

The Bohr theory of the hydrogen atom predicts the energy difference (in J) between the n = 3 and the n = 5 state to be

Use the Rydberg equation to calculate the frequency of a photon absorbed when the hydrogen atom undergoes a transition from n₁ = 2 to n₂ = 4. (R = 1.096776 × 10⁷ m⁻¹)

The de Broglie equation predicts that the wavelength (in m) of a proton moving at 1000. m/s is

According to the Rydberg equation, the line with the shortest wavelength in the emission spectrum of atomic hydrogen is predicted to lie at a wavelength (in nm) of

The ionization energy is the energy needed to remove an electron from an atom. In the Bohr model of the hydrogen atom, this means exciting the electron to the n = ∞ state. What is the ionization energy in kJ/mol, for hydrogen atoms initially in the n = 2 energy level?

A sprinter must average 24.0 mi/h to win a 100-m dash in 9.30 s. What is his wavelength at this speed if his mass is 84.5 kg?

Consider the following adjectives used to describe types of spectrum: continuous, line, atomic, emission and absorption.How many of them are appropriate to describe the spectrum of radiation given off by a black body?

According to the Rydberg equation, the longest wavelength (in nm) in the series of H-atom lines with n₁ = 3 is

What type of spectrum, if any, would be produced if the light radiated by a heated atomic gas were to be dispersed through a prism?

An electron in the n = 6 level emits a photon with a wavelength of 410.2 nm. To what energy level does the electron move?

For all the allowed vibration(s) (wavelength(s) ) of a plucked guitar string, what is the correct relationship between the length of the string, L, and the wavelength, λ?

According to the Heisenberg uncertainty principle, if the uncertainty in the speed of an electron is 3.5 × 10³ m/s, the uncertainty in its position (in m) is at least

For potassium metal, the work functionΦ (the minimum energy needed to eject an electron from the metal surface) is 3.68 × 10⁻¹⁹ J. Which is the longest wavelength of the following which could excite photoelectrons?

Consider the following adjectives used to describe types of spectrum: continuous, line, atomic, emission and absorption.How many of them are appropriate to describe the spectrum of radiation absorbed by a sample of mercury vapor?

According to the Bohr theory of the hydrogen atom, the minimum energy (in J) needed to ionize a hydrogen atom from the n = 2 state is

Quiz 7: Quantum Theory and Atomic Structure

Excited hydrogen atoms radiate energy in the

Platinum, which is widely used as a catalyst, has a work functionΦ (the minimum energy needed to eject an electron from the metal surface) of 9.05 × 10−19 J. What is the longest wavelength of light which will cause electrons to be emitted?

The size of an atomic orbital is associated with

The Bohr theory of the hydrogen atom predicts the energy difference (in J) between the n = 3 and the n = 5 state to be

Use the Rydberg equation to calculate the frequency of a photon absorbed when the hydrogen atom undergoes a transition from n1 = 2 to n2 = 4. (R = 1.096776 × 107 m−1)

The de Broglie equation predicts that the wavelength (in m) of a proton moving at 1000. m/s is

According to the Rydberg equation, the line with the shortest wavelength in the emission spectrum of atomic hydrogen is predicted to lie at a wavelength (in nm) of

The ionization energy is the energy needed to remove an electron from an atom. In the Bohr model of the hydrogen atom, this means exciting the electron to the n = ∞ state. What is the ionization energy in kJ/mol, for hydrogen atoms initially in the n = 2 energy level?

A sprinter must average 24.0 mi/h to win a 100-m dash in 9.30 s. What is his wavelength at this speed if his mass is 84.5 kg?

Consider the following adjectives used to describe types of spectrum: continuous, line, atomic, emission and absorption.How many of them are appropriate to describe the spectrum of radiation given off by a black body?

According to the Rydberg equation, the longest wavelength (in nm) in the series of H-atom lines with n1 = 3 is

What type of spectrum, if any, would be produced if the light radiated by a heated atomic gas were to be dispersed through a prism?

An electron in the n = 6 level emits a photon with a wavelength of 410.2 nm. To what energy level does the electron move?

For all the allowed vibration(s) (wavelength(s) ) of a plucked guitar string, what is the correct relationship between the length of the string, L, and the wavelength, λ?

According to the Heisenberg uncertainty principle, if the uncertainty in the speed of an electron is 3.5 × 103 m/s, the uncertainty in its position (in m) is at least

For potassium metal, the work functionΦ (the minimum energy needed to eject an electron from the metal surface) is 3.68 × 10−19 J. Which is the longest wavelength of the following which could excite photoelectrons?

Consider the following adjectives used to describe types of spectrum: continuous, line, atomic, emission and absorption.How many of them are appropriate to describe the spectrum of radiation absorbed by a sample of mercury vapor?

According to the Bohr theory of the hydrogen atom, the minimum energy (in J) needed to ionize a hydrogen atom from the n = 2 state is

Platinum, which is widely used as a catalyst, has a work functionΦ (the minimum energy needed to eject an electron from the metal surface) of 9.05 × 10⁻¹⁹ J. What is the longest wavelength of light which will cause electrons to be emitted?

Use the Rydberg equation to calculate the frequency of a photon absorbed when the hydrogen atom undergoes a transition from n₁ = 2 to n₂ = 4. (R = 1.096776 × 10⁷ m⁻¹)

According to the Rydberg equation, the longest wavelength (in nm) in the series of H-atom lines with n₁ = 3 is

According to the Heisenberg uncertainty principle, if the uncertainty in the speed of an electron is 3.5 × 10³ m/s, the uncertainty in its position (in m) is at least

For potassium metal, the work functionΦ (the minimum energy needed to eject an electron from the metal surface) is 3.68 × 10⁻¹⁹ J. Which is the longest wavelength of the following which could excite photoelectrons?