Question 1

The Bohr theory of the hydrogen atom predicts the energy difference (in J) between the n = 3 and the n = 5 state to be A) 8.72 × 10^-20 J. B) 1.36 × 10^-19 J. C) 2.42 × 10^-19 J. D) 1.55 × 10^-19 J. E) 1.09 × 10^-18 J.

Accepted Answer

The energy difference between two energy levels in the Bohr model is given by the formula ΔE = -Rh[(1/n₂²) - (1/n₁²)], where Rh is the Rydberg constant (2.18 x 10^-18 J), and n₁ and n₂ are the initial and final energy levels, respectively. Substituting n₁ = 3 and n₂ = 5, we get:
ΔE = -Rh[(1/5²) - (1/3²)] = 1.55 x 10^-19 J. Therefore, the correct answer is option D.

Question 2

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?
A) one
B) two
C) three
D) four
E) five

Accepted Answer

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

Question 3

Green light has a wavelength of 5200 Å. Calculate the energy of one photon of green light. A) 3.4 × 10^-40 J B) 3.4 × 10^-30 J C) 3.8 × 10^-29 J D) 3.4 × 10^-27 J E) 3.8 × 10^-19 J

Accepted Answer

The energy of a photon is calculated using the formula E = hc/λ, where h is Planck's constant (6.626 × 10^-34 J·s), c is the speed of light (3 × 10^8 m/s), and λ is the wavelength in meters (5200 Å = 5200 × 10^-10 m). Substituting these values gives E ≈ 3.8 × 10^-19 J.

Question 4

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) A) 2.056 × 10⁶ s^-1 B) 2.742 × 10⁶ s^-1 C) 6.165 × 10¹⁴ s^-1 D) 8.226 × 10¹⁴ s^-1 E) > 10¹⁵ s^-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 5

An infrared wave has a wavelength of 6.5 × 10^-4 cm. What is this distance in angstroms, Å? A) 6.5 × 10^-4 Å B) 2.2 × 10^-4 Å C) 4.6 × 10³ Å D) 6.5 × 10⁴ Å E) 6.5 × 10⁶ Å

Accepted Answer

1 cm equals 10^8 angstroms, so 6.5 × 10^-4 cm is 6.5 × 10^-4 × 10^8 Å = 6.5 × 10^4 Å.

Question 6

For potassium metal, the work function (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? A) 550. nm B) 500. nm C) 450. nm D) 400. nm E) 350. nm

Accepted Answer

The answer of For potassium metal, the work function ...

Question 7

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?
A) n = 1
B) n = 2
C) n = 3
D) n = 4
E) n = 5

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 8

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?
A) none
B) one
C) two
D) three
E) four

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 9

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) 91.2 nm. B) 1.10 × 10^-2 nm. C) 1.10 × 10² nm. D) 1.10 × 10¹⁶ nm. E) None of these choices are correct.

Accepted Answer

The shortest wavelength in the hydrogen emission spectrum corresponds to the transition from n = ∞ to n = 1, which is in the Lyman series. This wavelength is approximately 91.2 nm.

Question 10

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) A) 205.1 nm B) 384.6 nm C) 683.8 nm D) 1282 nm E) > 1500 nm

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 11

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?
A) a continuous band of color
B) a continuous band of color with some dark lines (missing wavelengths)
C) only blue light
D) only red light
E) discrete lines of different colors

Accepted Answer

When the light radiated by a heated atomic gas is dispersed through a prism, it produces a spectrum of discrete lines of different colors. This is because the atoms in the gas can only emit or absorb light at specific wavelengths, which correspond to the energy differences between different atomic energy levels. These discrete wavelengths appear as bright lines (emission) or dark lines (absorption) in the spectrum. This type of spectrum is known as a line spectrum or atomic spectrum.

Question 12

Platinum, which is widely used as a catalyst, has a work function (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? A) 2.196 × 10^-7 m B) 4.553 × 10^-6 m C) 5.654 × 10² m D) 1.370 × 10¹⁵ m E) > 10⁶ m

Accepted Answer

The energy of a photon of light is given by E=hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength of light. For an electron to be ejected from the platinum surface, the energy of the photon must be greater than or equal to the work function of platinum. Therefore, we can set E=hc/λ equal to the work function and solve for λ. This gives λ = hc/E = (6.626 × 10^-34 J s) (2.998 × 10^8 m/s) / (9.05 × 10^-19 J) = 2.196 × 10^-7 m. This wavelength corresponds to choice A.

Question 13

If the energy of a photon is 1.32 × 10^-18 J, what is its wavelength in nm? A) 1.50 × 10^-7 nm B) 150. nm C) 1.99 × 10¹⁵ nm D) 1.99 × 10²⁴ nm E) None of these choices are correct.

Accepted Answer

The energy of a photon is given by E = hc/λ, where h is Planck's constant (6.626 × 10^-34 J·s) and c is the speed of light (3.00 × 10^8 m/s). Solving for λ gives λ = hc/E. Substituting the given energy and constants, λ = (6.626 × 10^-34 J·s)(3.00 × 10^8 m/s) / (1.32 × 10^-18 J) = 1.50 × 10^-7 m, which is 150 nm.

Question 14

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? A) 7.8 × 10^-19 J B) 3.3 J C) 6.6 × 10² J D) 3.3 × 10³ J E) 4.2 × 10¹⁸ J

Accepted Answer

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

Question 15

Infrared radiation from the sun has a wavelength of 6200 nm. Calculate the energy of one photon of that radiation. A) 4.l × 10^-39 J B) 4.l × 10^-30 J C) 3.2 × 10^-29 J D) 3.2 × 10^-26 J E) between 10^-20 and 10^-19 J

Accepted Answer

The energy of a photon is calculated using the formula E = hc/λ, where h is Planck's constant (6.626 × 10^-34 J·s), c is the speed of light (3 × 10^8 m/s), and λ is the wavelength in meters (6200 nm = 6.2 × 10^-6 m). This calculation results in an energy value between 10^-20 and 10^-19 J.

Question 16

According to the Rydberg equation, the longest wavelength (in nm) in the series of H-atom lines with n₁ = 3 is A) 1875 nm. B) 1458 nm. C) 820. nm. D) 656 nm. E) 365 nm.

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 17

A photon has an energy of 5.53 × 10^-17 J. What is its frequency in s^-1? A) 3.66 × 10^-50 s^-1 B) 1.20 × 10^-17 s^-1 C) 3.59 × 10^-9 s^-1 D) 2.78 × 10⁸ s^-1 E) 8.35 × 10¹⁶ s^-1

Accepted Answer

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

Question 18

A radio wave has a frequency of 8.6 × 10⁸ Hz. What is the energy of one photon of this radiation? A) 7.7 × 10^-43 J B) 2.3 × 10^-34 J C) 5.7 × 10^-25 J D) 1.7 × 10^-16 J E) > 10^-15 J

Accepted Answer

The energy of a photon is calculated using the formula E = hν, where h is Planck's constant (6.626 × 10^-34 J·s) and ν is the frequency. Substituting the given frequency, E = 6.626 × 10^-34 J·s × 8.6 × 10^8 Hz = 5.7 × 10^-25 J.

Question 19

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? A) 3.7 × 10¹⁴ m/s B) 3.7 × 10¹¹ m/s C) 1.9 × 10⁶ m/s D) 6.1 × 10⁵ m/s E) 1.7 × 10^-19 m/s

Accepted Answer

Using conservation of energy:

Energy of photon = Work function + Kinetic energy of photoelectron

5.3 × 10^-19 J = 3.6 × 10^-19 J + (1/2)mv^2

Solving for v:

v = sqrt[(2(5.3 × 10^-19 J - 3.6 × 10^-19 J)/m)]

The mass of an electron is 9.11 × 10^-31 kg. Plugging this in:

v = 6.1 × 10^5 m/s

Rounding to two significant figures, the answer is 6.1 × 10^5 m/s or 6.1 × 10^15 m/s.

Question 20

Excited hydrogen atoms radiate energy in the
A) infrared region only.
B) visible region only.
C) ultraviolet region only.
D) visible and ultraviolet regions only.
E) infrared, visible, and ultraviolet regions.

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.

Quiz 7: Quantum Theory and Atomic Structure

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

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?

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

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)

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

For potassium metal, the work function (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?

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?

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?

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

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?

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

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?

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

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

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

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

Excited hydrogen atoms radiate energy in the

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)

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

For potassium metal, the work function (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?

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

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

A photon has an energy of 5.53 × 10^-17 J. What is its frequency in s^-1?

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