A metal foil has a threshold frequency of 5.45 x 10^14 Hz. Which color of visible light will not eject electrons from this metal? a) blue b) indigo c) violet d) orange c = (wavelength)(v) 3.0 x 10^8 m/s = (wavelength)(5.45 x 10^14 Hz) 550 nm -> releases green. So, I am guessing the answer would be d) orange.
The Correct Answer and Explanation is:
To answer this question, we need to relate the threshold frequency to the energy required for the photoelectric effect to occur and then determine the color of visible light that corresponds to frequencies below this threshold.
Key Concepts:
- Photoelectric Effect: For the photoelectric effect to occur, the frequency of the incoming light must be higher than the threshold frequency of the material. If the frequency of the light is lower than the threshold, no electrons will be ejected.
- Threshold Frequency: This is the minimum frequency of light required to release electrons from the metal’s surface. The threshold frequency for the metal in question is 5.45×1014 Hz5.45 \times 10^{14} \, \text{Hz}5.45×1014Hz.
- Speed of Light Equation: The equation relating the speed of light, frequency, and wavelength is given by: c=λ⋅vc = \lambda \cdot vc=λ⋅v where:
- ccc is the speed of light (3.0×108 m/s3.0 \times 10^8 \, \text{m/s}3.0×108m/s),
- λ\lambdaλ is the wavelength,
- vvv is the frequency.
- Color and Frequency: The frequency of visible light corresponds to different colors, with violet having the highest frequency and red (or orange) having the lowest. A higher frequency light (like violet) has more energy, while lower frequency light (like orange) has less energy.
Step-by-step:
- We are given the threshold frequency as 5.45×1014 Hz5.45 \times 10^{14} \, \text{Hz}5.45×1014Hz.
- To find which colors will not eject electrons, we need to check the frequencies of the different colors in the visible spectrum and compare them with the threshold frequency.
Now, let’s check the frequencies of the colors:
- Violet: Around 7.5×1014 Hz7.5 \times 10^{14} \, \text{Hz}7.5×1014Hz (higher than the threshold, will eject electrons)
- Indigo: Around 6.9×1014 Hz6.9 \times 10^{14} \, \text{Hz}6.9×1014Hz (higher than the threshold, will eject electrons)
- Blue: Around 6.0×1014 Hz6.0 \times 10^{14} \, \text{Hz}6.0×1014Hz (higher than the threshold, will eject electrons)
- Green: Around 5.5×1014 Hz5.5 \times 10^{14} \, \text{Hz}5.5×1014Hz (approximately equal to threshold, may or may not eject electrons)
- Orange: Around 4.5×1014 Hz4.5 \times 10^{14} \, \text{Hz}4.5×1014Hz (lower than the threshold, will not eject electrons)
Conclusion:
Since the threshold frequency is 5.45×1014 Hz5.45 \times 10^{14} \, \text{Hz}5.45×1014Hz, and the frequency of orange light is lower than this threshold, orange light will not have enough energy to eject electrons. Therefore, the correct answer is:
d) orange.
This is because the frequency of orange light is below the threshold frequency required for the photoelectric effect to occur.
