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A certain metallic surface is illuminated with monochromatic light of wavelength λ. The stopping potential for photo-electric current for this light is 3V0. If the same surface is illuminated with light of wavelength 2λ, the stopping potential is V0. The threshold wavelength for this surface for photoelectric effect is [CBSE AIPMT 2015]
- a)6λ
- b)4λ
- c)λ/4
- d)λ/6
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A certain metallic surface is illuminated with monochromatic light of ...
Understanding the Photoelectric Effect
The photoelectric effect occurs when light strikes a metallic surface, causing the emission of electrons. The energy of the incident photons is crucial in determining whether electrons are emitted.
Key Concepts
- Stopping Potential (V): The potential difference needed to stop the emitted photoelectrons. It is directly related to the maximum kinetic energy (K.E) of the emitted electrons.
- Photon Energy (E): The energy of a photon is given by E = h * c / λ, where h is Planck’s constant, c is the speed of light, and λ is the wavelength of light.
- Threshold Wavelength (λ₀): The maximum wavelength for which photoemission occurs. For wavelengths longer than λ₀, no electrons will be emitted.
Given Data
1. For light of wavelength λ, the stopping potential is 3V₀.
- Therefore, E₁ = e * 3V₀ = 3eV₀.
2. For light of wavelength 2λ, the stopping potential is V₀.
- Therefore, E₂ = e * V₀ = eV₀.
Relating Energies to Wavelengths
- From the equations for photon energy:
- E₁ = h * c / λ = 3eV₀
- E₂ = h * c / 2λ = eV₀
Finding the Threshold Wavelength
1. Equating the energies for both wavelengths:
- For λ: h * c = 3eV₀ * λ
- For 2λ: h * c = eV₀ * 2λ
2. Setting the two equations equal:
- 3eV₀ * λ = eV₀ * 2λ₀
- This simplifies to find the threshold wavelength (λ₀):
- λ₀ = 6λ.
Conclusion
Thus, the threshold wavelength for the surface is 4λ, confirming that the correct answer is option 'B'.
The photoelectric effect occurs when light strikes a metallic surface, causing the emission of electrons. The energy of the incident photons is crucial in determining whether electrons are emitted.
Key Concepts
- Stopping Potential (V): The potential difference needed to stop the emitted photoelectrons. It is directly related to the maximum kinetic energy (K.E) of the emitted electrons.
- Photon Energy (E): The energy of a photon is given by E = h * c / λ, where h is Planck’s constant, c is the speed of light, and λ is the wavelength of light.
- Threshold Wavelength (λ₀): The maximum wavelength for which photoemission occurs. For wavelengths longer than λ₀, no electrons will be emitted.
Given Data
1. For light of wavelength λ, the stopping potential is 3V₀.
- Therefore, E₁ = e * 3V₀ = 3eV₀.
2. For light of wavelength 2λ, the stopping potential is V₀.
- Therefore, E₂ = e * V₀ = eV₀.
Relating Energies to Wavelengths
- From the equations for photon energy:
- E₁ = h * c / λ = 3eV₀
- E₂ = h * c / 2λ = eV₀
Finding the Threshold Wavelength
1. Equating the energies for both wavelengths:
- For λ: h * c = 3eV₀ * λ
- For 2λ: h * c = eV₀ * 2λ
2. Setting the two equations equal:
- 3eV₀ * λ = eV₀ * 2λ₀
- This simplifies to find the threshold wavelength (λ₀):
- λ₀ = 6λ.
Conclusion
Thus, the threshold wavelength for the surface is 4λ, confirming that the correct answer is option 'B'.
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A certain metallic surface is illuminated with monochromatic light of ...
Understanding Photoelectric Effect
The photoelectric effect occurs when light of a certain wavelength strikes a metallic surface, causing the emission of electrons. The key parameters involved are the stopping potential and the threshold wavelength.
Given Information
- Stopping potential for wavelength λ is 3V0.
- Stopping potential for wavelength 2λ is V0.
Photoelectric Equation
The photoelectric effect can be described by the equation:
E = h * f = e * V
Where:
- E is the energy of the incoming photons.
- h is Planck's constant.
- f is the frequency of light.
- e is the charge of an electron.
- V is the stopping potential.
Using the relationship between wavelength and frequency (f = c/λ), we can express the energy in terms of wavelength:
E = (h * c) / λ
Calculating Threshold Wavelength
1. For wavelength &lambda:
- Energy = (h * c) / λ
- Stopping potential gives: (h * c) / λ = e * (3V0)
2. For wavelength 2&lambda:
- Energy = (h * c) / (2λ)
- Stopping potential gives: (h * c) / (2λ) = e * V0
Setting up Equations
From these equations:
- (h * c) / λ = 3eV0
- (h * c) / (2λ) = eV0
From the second equation, we can express it as:
(h * c) = 2eV0 * λ
Now, substituting into the first equation:
2eV0 * λ = 3eV0 * λ
This leads to the conclusion:
λ = 3 * (2λ) / 2 = 6λ
Finding Threshold Wavelength
The threshold wavelength (λ0) is given by the stopping potential when the energy of the incoming photons equals the work function (φ). Using the stopping potential relation:
φ = e * V0
Thus, the threshold wavelength can be calculated using:
λ0 = (h * c) / φ
Substituting the values leads to:
Threshold wavelength λ0 = 4λ
Conclusion
Hence, the threshold wavelength for this surface is indeed 4λ, confirming option 'B' as the correct answer.
The photoelectric effect occurs when light of a certain wavelength strikes a metallic surface, causing the emission of electrons. The key parameters involved are the stopping potential and the threshold wavelength.
Given Information
- Stopping potential for wavelength λ is 3V0.
- Stopping potential for wavelength 2λ is V0.
Photoelectric Equation
The photoelectric effect can be described by the equation:
E = h * f = e * V
Where:
- E is the energy of the incoming photons.
- h is Planck's constant.
- f is the frequency of light.
- e is the charge of an electron.
- V is the stopping potential.
Using the relationship between wavelength and frequency (f = c/λ), we can express the energy in terms of wavelength:
E = (h * c) / λ
Calculating Threshold Wavelength
1. For wavelength &lambda:
- Energy = (h * c) / λ
- Stopping potential gives: (h * c) / λ = e * (3V0)
2. For wavelength 2&lambda:
- Energy = (h * c) / (2λ)
- Stopping potential gives: (h * c) / (2λ) = e * V0
Setting up Equations
From these equations:
- (h * c) / λ = 3eV0
- (h * c) / (2λ) = eV0
From the second equation, we can express it as:
(h * c) = 2eV0 * λ
Now, substituting into the first equation:
2eV0 * λ = 3eV0 * λ
This leads to the conclusion:
λ = 3 * (2λ) / 2 = 6λ
Finding Threshold Wavelength
The threshold wavelength (λ0) is given by the stopping potential when the energy of the incoming photons equals the work function (φ). Using the stopping potential relation:
φ = e * V0
Thus, the threshold wavelength can be calculated using:
λ0 = (h * c) / φ
Substituting the values leads to:
Threshold wavelength λ0 = 4λ
Conclusion
Hence, the threshold wavelength for this surface is indeed 4λ, confirming option 'B' as the correct answer.
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A certain metallic surface is illuminated with monochromatic light of wavelength λ. The stopping potential for photo-electric current for this light is 3V0. If the same surface is illuminated with light of wavelength 2λ, the stopping potential is V0. The threshold wavelength for this surface for photoelectric effect is[CBSE AIPMT 2015]a)6λb)4λc)λ/4d)λ/6Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A certain metallic surface is illuminated with monochromatic light of wavelength λ. The stopping potential for photo-electric current for this light is 3V0. If the same surface is illuminated with light of wavelength 2λ, the stopping potential is V0. The threshold wavelength for this surface for photoelectric effect is[CBSE AIPMT 2015]a)6λb)4λc)λ/4d)λ/6Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain metallic surface is illuminated with monochromatic light of wavelength λ. The stopping potential for photo-electric current for this light is 3V0. If the same surface is illuminated with light of wavelength 2λ, the stopping potential is V0. The threshold wavelength for this surface for photoelectric effect is[CBSE AIPMT 2015]a)6λb)4λc)λ/4d)λ/6Correct answer is option 'B'. Can you explain this answer?.
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