Question 1

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 × 10¹⁴s^-1 D) 8.226 × 10¹⁴ s^-1 E) > 10¹⁵ s^-1

Accepted Answer

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Question 2

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^-30J C) 3.8 × 10^-29 J D) 3.4 × 10^-27 J E) 3.8 × 10^-19 J

Accepted Answer

The answer of Green light has a wavelength of 5200...

Question 3

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 =$\infty$ state. What is the ionization energy in kJ/mol, for hydrogen atoms initially in the n = 2 energy level?
A) 290 kJ/mol
B) 328 kJ/mol
C) 656 kJ/mol
D) 983 kJ/mol
E) 1311 kJ/mol

Accepted Answer

The ionization energy of the hydrogen atom can be calculated using the following equation:

Ionization energy = (-Rh) * (1/n^2_final - 1/n^2_initial)

Where Rh is the Rydberg constant (2.18 x 10^-18 J), n_final is the final energy level (infinity for ionization), and n_initial is the initial energy level (2 in this case).

Plugging in the values, we get:

Ionization energy = (-2.18 x 10^-18 J) * (1/∞ - 1/2^2)
Ionization energy = 328 kJ/mol

Therefore, the best choice is B.

Question 4

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 A) 2.18 × 10^-18J. B) 1.64 × 10^-18J. C) 5.45 × 10^-19J. D) 3.03 × 10^-19J. E) none of the above.

Accepted Answer

According to the Bohr theory, the energy required to ionize a hydrogen atom from the n = 2 state is given by:

E = -RH(1/nf^2 - 1/ni^2)

where RH is the Rydberg constant, nf is the final state (in this case, infinity), and ni is the initial state (in this case, 2). Plugging in the values, we get:

E = -2.18 x 10^-18 J (1/∞^2 - 1/2^2)
E = 5.45 x 10^-19 J

Therefore, the answer is C: 5.45 x 10^-19 J.

Question 5

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

First, we calculate the energy of the photoelectron by subtracting the minimum energy required for the electron to escape from the metal (3.6 × 10^-19 J) from the initial energy of the photon (5.3 × 10^-19 J):

5.3 × 10^-19 J - 3.6 × 10^-19 J = 1.7 × 10^-19 J

This remaining energy appears as kinetic energy of the photoelectron. We can use the equation for kinetic energy to calculate the velocity of the photoelectron:

KE = 1/2 mv^2

Where KE is the kinetic energy of the photoelectron, m is the mass of the electron, and v is the velocity of the photoelectron. We can rearrange this equation to solve for v:

v = sqrt(2KE/m)

We know the mass of the electron (9.11 × 10^-31 kg) and we just calculated the kinetic energy of the photoelectron (1.7 × 10^-19 J). Plugging in these values, we get:

v = sqrt(2(1.7 × 10^-19 J)/(9.11 × 10^-31 kg)) = 6.1 × 10^5 m/s

So the correct answer is D.

Question 6

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 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

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? 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 longest wavelength corresponds to the minimum energy needed to eject an electron, which is given by the work function. Using the equation λ = hc/ϕ, 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), we find λ = (6.626 × 10^-34 J·s * 3.00 × 10^8 m/s) / 9.05 × 10^-19 J = 2.196 × 10^-7 m.

Question 9

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 10

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

The light radiated by a atomic gas would produce a line spectrum or an emission spectrum. This is because the atoms in the gas can only emit certain wavelengths of light corresponding to the energy differences between their electron orbitals. When this light is dispersed through a prism, it will appear as discrete lines of different colors, rather than a continuous band of color or only one or two colors.

Question 11

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 12

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 answer of Line spectra from all regions of the...

Question 13

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^-43J B) 2.3 × 10^-34 J C) 5.7 × 10^-25 J D) 1.7 × 10^-16J E) > 10^-15J

Accepted Answer

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

Question 14

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.

Question 15

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? A) 550. nm B) 500. nm C) 450. nm D) 400. nm E) 350. nm

Accepted Answer

The energy of a photon is given by E = hc/λ. To eject an electron, this energy must be at least equal to the work function. Using the given work function, the longest wavelength that can excite photoelectrons is calculated to be approximately 500 nm.

Question 16

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

The answer of An infrared wave has a wavelength of...

Question 17

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 × 10²nm. D) 1.10 × 10¹⁶nm. E) none of the above.

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. The Rydberg formula gives this wavelength as approximately 91.2 nm.

Question 18

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

Accepted Answer

The answer of A photon has an energy of 5.53...

Question 19

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 20

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^-20J. B) 1.36 × 10^-19J. C) 2.42 × 10^-19J. D) 1.55 × 10^-19J. E) 1.09 × 10^-18J.

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.

Quiz 7: Quantum Theory and Atomic Structure

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)

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

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 = $\infty$ state. What is the ionization energy in kJ/mol, for hydrogen atoms initially in the n = 2 energy level?

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

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?

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?

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?

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?

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?

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?

Excited hydrogen atoms radiate energy in the

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?

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

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?

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?

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