Question 1

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 2

A radio wave has a frequency of 8.6 * 10⁸ Hz. What is the energy of one photon of this radiation?

Accepted Answer

The answer of A radio wave has a frequency of...

Question 3

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

According to the Bohr theory, the energy difference between two energy levels can be calculated using the formula:
ΔE = -Rhc/ni² + Rhc/nf²
where R is the Rydberg constant, h is Planck's constant, c is the speed of light, ni and nf are the initial and final energy levels (in this case, n=3 and n=5).
Plugging in the values:
ΔE = -Rhc/3² + Rhc/5² = -13.6 eV * (1.6 × 10^-19 J/eV) * (2.998 × 10^8 m/s) / 3² + 13.6 eV * (1.6 × 10^-19 J/eV) * (2.998 × 10^8 m/s) / 5²
ΔE = 1.55 × 10^-18 J, which is answer choice D.

Question 4

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

When light radiated by an atomic gas is dispersed through a prism, it produces a line spectrum consisting of discrete lines of different colors. This is because each element emits light at only specific wavelengths, which correspond to the energy differences between electron energy levels in the atoms. These discrete lines appear as bright lines against a dark background, since only specific wavelengths (colors) of light are emitted by the atoms.

Question 5

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

Accepted Answer

The answer of Consider the following adjectives used to describe...

Question 6

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 shortest wavelength in the hydrogen emission spectrum corresponds to the transition to the n=1 level, known as the Lyman series limit, which is approximately 91.2 nm.

Question 7

A photon has an energy of 5.53 * 10¯¹⁷ J. What is its frequency in s¯¹?

Accepted Answer

The frequency of a photon can be calculated using the formula E = hν, where E is the energy, h is Planck's constant (6.626 x 10^-34 J·s), and ν is the frequency. Solving for ν gives ν = E/h = (5.53 x 10^-17 J) / (6.626 x 10^-34 J·s) = 8.35 x 10^16 s^-1.

Question 8

Platinum, which is widely used as a catalyst, has a work function $\phi$ (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 corresponds to the lowest energy photon that can eject an electron. Using the equation $ \lambda = \frac{hc}{\phi} $, where $ h $ is Planck's constant and $ c $ is the speed of light, we find the wavelength to be approximately 2.196 * 10¯⁷ m.

Question 9

If the energy of a photon is 1.32 *10¯¹⁸ J, what is its wavelength in nm?

Accepted Answer

The answer of If the energy of a photon is...

Question 10

For potassium metal, the work function $\phi$ (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 energy of a photon is given by $E = \frac{hc}{\lambda}$. To eject an electron, the photon energy must be at least equal to the work function. For $\phi = 3.68 \times 10^{-19}$ J, the longest wavelength $\lambda$ is calculated using $\lambda = \frac{hc}{\phi}$. This gives approximately 540 nm, so 500 nm is the longest wavelength from the given options that can excite photoelectrons.

Question 11

Infrared radiation from the sun has a wavelength of 6200 nm. Calculate the energy of one photon of that radiation.

Accepted Answer

The energy of a photon is calculated using E = hc/λ. With λ = 6200 nm = 6200 x 10^-9 m, h = 6.626 x 10^-34 J·s, and c = 3 x 10^8 m/s, the energy is approximately between 10^-20 and 10^-19 J.

Question 12

Consider the following adjectives used to describe types of spectrum: continuous, line, atomic, emission, 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 is a continuous spectrum, as all wavelengths of electromagnetic radiation are emitted.
It is also an emission spectrum, as the black body emits radiation rather than absorbing it.
Therefore, two adjectives are appropriate to describe the spectrum of radiation given off by a black body: continuous and emission.

Question 13

A modern compact fluorescent lamp contains 1.4 mg of mercury. If each mercury atom in the lamp were to emit a single photon of wavelength 254 nm, how many joules of energy would be emitted?

Accepted Answer

The answer of A modern compact fluorescent lamp contains 1.4...

Question 14

An infrared wave has a wavelength of 6.5 * 10¯⁴ cm. What is this distance in angstroms, Å?

Accepted Answer

1 Å = 10^-8 cm(6.5 * 10^-4 cm) * (1 Å / 10^-8 cm) = 6.5 * 10⁴ Å

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

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's emission lines. For the Paschen series (transitions to n = 3), the formula is 1/λ = R * (1/3² - 1/5²). Plugging in the values, we find λ ≈ 1282 nm.

Question 17

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 18

Green light has a wavelength of 5200 Å. Calculate the energy of one photon of green light.

Accepted Answer

The energy of a photon is 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 x 10^8 m/s), and λ is the wavelength in meters (5200 Å = 5200 x 10^-10 m). Substituting these values gives E ≈ 3.8 x 10^-19 J.

Question 19

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 formula for frequency is 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 20

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 answer of In the photoelectric effect, a photon with...

Quiz 7: Quantum Theory and Atomic Structure

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

A radio wave has a frequency of 8.6 * 108 Hz. What is the energy of one photon of this radiation?

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

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?

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

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:

A photon has an energy of 5.53 * 10¯17 J. What is its frequency in s¯1?

Platinum, which is widely used as a catalyst, has a work function ϕ\phiϕ (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?

If the energy of a photon is 1.32 *10¯18 J, what is its wavelength in nm?

For potassium metal, the work function ϕ\phiϕ (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?