Question
Light with a wavelength of 725 nm passed through this list of a double-slit experiment. The slits of the experiment are a distance of 0.0335 mm apart. What angle does the light make for the third dark fringe?
Hint: sinθ=mλd, m=0,1,2,3...
, make sure the distances are converted meters.
(1 point)
Responses
4.96°
4.96°
2.48°
2.48°
1.24°
1.24°
3.10°
3.10°
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Question
When studying the photoelectric effect, which parameters did scientists think were relevant for electrons to be released or not in both the wave and particle models?(1 point)
Responses
frequency only for both models
frequency only for both models
intensity only for both models
intensity only for both models
frequency and intensity for the wave model; frequency only for the part of the model
frequency and intensity for the wave model; frequency only for the part of the model
frequency and intensity for the particle model; frequency only for the wave model
frequency and intensity for the particle model; frequency only for the wave model
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Question
Use the image to answer the question.
A dashed line at the bottom depicts the lowest energy level (normal state). A dashed line at some vertical distance shows a specific energy level. If an electron absorbs that much energy, it escapes from the atom, and the atom is ionized. The vertical lines at the top show the highest energy level (ionized).
The image represents the gaps between allowed energy levels for electrons. Which model best describes this phenomenon?
(1 point)
Responses
the wave model because the arrows show that the energy transfers continuous
the wave model because the arrows show that the energy transfers continuous
the wave model because electrons orbit the atom's nucleus in a continuous way
the wave model because electrons orbit the atom's nucleus in a continuous way
the particle model because the arrows represent discrete particle like jumps
the particle model because the arrows represent discrete particle like jumps
the particle model because electrons are particles
the particle model because electrons are particles
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Hint: sinθ=mλd, m=0,1,2,3...
, make sure the distances are converted meters.
(1 point)
Responses
4.96°
4.96°
2.48°
2.48°
1.24°
1.24°
3.10°
3.10°
Skip to navigation
Question
When studying the photoelectric effect, which parameters did scientists think were relevant for electrons to be released or not in both the wave and particle models?(1 point)
Responses
frequency only for both models
frequency only for both models
intensity only for both models
intensity only for both models
frequency and intensity for the wave model; frequency only for the part of the model
frequency and intensity for the wave model; frequency only for the part of the model
frequency and intensity for the particle model; frequency only for the wave model
frequency and intensity for the particle model; frequency only for the wave model
Skip to navigation
Question
Use the image to answer the question.
A dashed line at the bottom depicts the lowest energy level (normal state). A dashed line at some vertical distance shows a specific energy level. If an electron absorbs that much energy, it escapes from the atom, and the atom is ionized. The vertical lines at the top show the highest energy level (ionized).
The image represents the gaps between allowed energy levels for electrons. Which model best describes this phenomenon?
(1 point)
Responses
the wave model because the arrows show that the energy transfers continuous
the wave model because the arrows show that the energy transfers continuous
the wave model because electrons orbit the atom's nucleus in a continuous way
the wave model because electrons orbit the atom's nucleus in a continuous way
the particle model because the arrows represent discrete particle like jumps
the particle model because the arrows represent discrete particle like jumps
the particle model because electrons are particles
the particle model because electrons are particles
Skip to navigation
Answers
GPT-4o mini
Let's address each question one by one.
### 1. Angle for the Third Dark Fringe in a Double-Slit Experiment
In a double-slit experiment, the condition for dark fringes (destructive interference) is given by the formula:
\[
d \sin \theta = (m + 0.5) \lambda
\]
where:
- \(d\) is the distance between the slits (in meters),
- \(\lambda\) is the wavelength of the light (in meters),
- \(m\) is the order of the dark fringe (0, 1, 2, ...).
You've mentioned the third dark fringe, so \(m = 2\).
Given:
- Wavelength, \(\lambda = 725 \, \text{nm} = 725 \times 10^{-9} \, \text{m}\)
- Distance between slits, \(d = 0.0335 \, \text{mm} = 0.0335 \times 10^{-3} \, \text{m}\)
Now, substituting these values into the dark fringe condition:
\[
0.0335 \times 10^{-3} \sin \theta = (2 + 0.5) (725 \times 10^{-9})
\]
\[
0.0335 \times 10^{-3} \sin \theta = 2.5 \times 725 \times 10^{-9}
\]
\[
0.0335 \times 10^{-3} \sin \theta = 1.8125 \times 10^{-6}
\]
Now, solve for \(\sin \theta\):
\[
\sin \theta = \frac{1.8125 \times 10^{-6}}{0.0335 \times 10^{-3}} \approx 0.0541
\]
Now, we can find \(\theta\):
\[
\theta = \sin^{-1}(0.0541) \approx 3.10^{\circ}
\]
**Answer: 3.10°**
---
### 2. Photoelectric Effect and Relevant Parameters
In the photoelectric effect:
- The wave model suggests that both frequency and intensity of light are important. However, it was later shown that only frequency (and not intensity) is relevant when considering the release of electrons in the context of the particle model.
- The particle model shows that photons must have a frequency above a certain threshold to release electrons, regardless of their intensity.
Thus, the best summary of ideas would be:
**Answer: frequency and intensity for the wave model; frequency only for the particle model.**
---
### 3. Energy Levels and Models
The description of energy levels and the absorption of energy leading to ionization implies discrete jumps between energy levels.
- This is best described by the particle model because the idea involves quantized energy states for electrons and the absorption of specific energy amounts (photons) to make these discrete transitions.
Therefore, the most appropriate answer is:
**Answer: the particle model because the arrows represent discrete particle-like jumps.**
If you have any further questions or need clarifications, feel free to ask!
### 1. Angle for the Third Dark Fringe in a Double-Slit Experiment
In a double-slit experiment, the condition for dark fringes (destructive interference) is given by the formula:
\[
d \sin \theta = (m + 0.5) \lambda
\]
where:
- \(d\) is the distance between the slits (in meters),
- \(\lambda\) is the wavelength of the light (in meters),
- \(m\) is the order of the dark fringe (0, 1, 2, ...).
You've mentioned the third dark fringe, so \(m = 2\).
Given:
- Wavelength, \(\lambda = 725 \, \text{nm} = 725 \times 10^{-9} \, \text{m}\)
- Distance between slits, \(d = 0.0335 \, \text{mm} = 0.0335 \times 10^{-3} \, \text{m}\)
Now, substituting these values into the dark fringe condition:
\[
0.0335 \times 10^{-3} \sin \theta = (2 + 0.5) (725 \times 10^{-9})
\]
\[
0.0335 \times 10^{-3} \sin \theta = 2.5 \times 725 \times 10^{-9}
\]
\[
0.0335 \times 10^{-3} \sin \theta = 1.8125 \times 10^{-6}
\]
Now, solve for \(\sin \theta\):
\[
\sin \theta = \frac{1.8125 \times 10^{-6}}{0.0335 \times 10^{-3}} \approx 0.0541
\]
Now, we can find \(\theta\):
\[
\theta = \sin^{-1}(0.0541) \approx 3.10^{\circ}
\]
**Answer: 3.10°**
---
### 2. Photoelectric Effect and Relevant Parameters
In the photoelectric effect:
- The wave model suggests that both frequency and intensity of light are important. However, it was later shown that only frequency (and not intensity) is relevant when considering the release of electrons in the context of the particle model.
- The particle model shows that photons must have a frequency above a certain threshold to release electrons, regardless of their intensity.
Thus, the best summary of ideas would be:
**Answer: frequency and intensity for the wave model; frequency only for the particle model.**
---
### 3. Energy Levels and Models
The description of energy levels and the absorption of energy leading to ionization implies discrete jumps between energy levels.
- This is best described by the particle model because the idea involves quantized energy states for electrons and the absorption of specific energy amounts (photons) to make these discrete transitions.
Therefore, the most appropriate answer is:
**Answer: the particle model because the arrows represent discrete particle-like jumps.**
If you have any further questions or need clarifications, feel free to ask!