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When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to:
Correct answer is '0.62'. Can you explain this answer?
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When the wavelength of radiation falling on a metal is changed from 50...
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When the wavelength of radiation falling on a metal is changed from 50...
Given:
- Wavelength of radiation (λ1) = 500 nm
- Wavelength of radiation (λ2) = 200 nm
- Change in maximum kinetic energy (ΔK.E.) = 3 times larger
To find:
- Work function of the metal (ϕ)
Explanation:
The photoelectric effect refers to the emission of electrons from a metal surface when it is exposed to electromagnetic radiation. The energy of the emitted electrons is determined by the energy of the incident photons, which is dependent on the wavelength of the radiation.
1. Calculation of initial energy:
- The energy (E) of a photon is given by the equation E = hc/λ, where h is Planck's constant (6.626 x 10^-34 J.s) and c is the speed of light (3 x 10^8 m/s).
- For the initial wavelength (λ1 = 500 nm = 500 x 10^-9 m), the energy of the photon (E1) is:
E1 = hc/λ1 = (6.626 x 10^-34 J.s x 3 x 10^8 m/s)/(500 x 10^-9 m) = 3.9768 x 10^-19 J
2. Calculation of final energy:
- For the final wavelength (λ2 = 200 nm = 200 x 10^-9 m), the energy of the photon (E2) is:
E2 = hc/λ2 = (6.626 x 10^-34 J.s x 3 x 10^8 m/s)/(200 x 10^-9 m) = 9.939 x 10^-19 J
3. Calculation of change in energy:
- The change in energy (ΔE) is given by the equation ΔE = E2 - E1:
ΔE = 9.939 x 10^-19 J - 3.9768 x 10^-19 J = 5.9622 x 10^-19 J
4. Calculation of work function:
- According to the photoelectric effect, the maximum kinetic energy (K.E.) of the emitted electrons is given by the equation K.E. = ΔE - ϕ, where ϕ is the work function.
- Given that the change in kinetic energy (ΔK.E.) is three times larger, we can write: ΔK.E. = 3(K.E.) = 3(ΔE - ϕ)
- Substituting the value of ΔE, we get: 3(5.9622 x 10^-19 J) = 5.9622 x 10^-19 J - 3ϕ
- Rearranging the equation, we find: 3ϕ = 3(5.9622 x 10^-19 J) - 5.9622 x 10^-19 J
⇒ 3ϕ = 11.9244 x 10^-19 J - 5.9622 x 10^-19 J
⇒ 3ϕ = 5.9622 x 10^-19 J
⇒ ϕ = (5.9622 x 10^-19 J)/3 ≈
- Wavelength of radiation (λ1) = 500 nm
- Wavelength of radiation (λ2) = 200 nm
- Change in maximum kinetic energy (ΔK.E.) = 3 times larger
To find:
- Work function of the metal (ϕ)
Explanation:
The photoelectric effect refers to the emission of electrons from a metal surface when it is exposed to electromagnetic radiation. The energy of the emitted electrons is determined by the energy of the incident photons, which is dependent on the wavelength of the radiation.
1. Calculation of initial energy:
- The energy (E) of a photon is given by the equation E = hc/λ, where h is Planck's constant (6.626 x 10^-34 J.s) and c is the speed of light (3 x 10^8 m/s).
- For the initial wavelength (λ1 = 500 nm = 500 x 10^-9 m), the energy of the photon (E1) is:
E1 = hc/λ1 = (6.626 x 10^-34 J.s x 3 x 10^8 m/s)/(500 x 10^-9 m) = 3.9768 x 10^-19 J
2. Calculation of final energy:
- For the final wavelength (λ2 = 200 nm = 200 x 10^-9 m), the energy of the photon (E2) is:
E2 = hc/λ2 = (6.626 x 10^-34 J.s x 3 x 10^8 m/s)/(200 x 10^-9 m) = 9.939 x 10^-19 J
3. Calculation of change in energy:
- The change in energy (ΔE) is given by the equation ΔE = E2 - E1:
ΔE = 9.939 x 10^-19 J - 3.9768 x 10^-19 J = 5.9622 x 10^-19 J
4. Calculation of work function:
- According to the photoelectric effect, the maximum kinetic energy (K.E.) of the emitted electrons is given by the equation K.E. = ΔE - ϕ, where ϕ is the work function.
- Given that the change in kinetic energy (ΔK.E.) is three times larger, we can write: ΔK.E. = 3(K.E.) = 3(ΔE - ϕ)
- Substituting the value of ΔE, we get: 3(5.9622 x 10^-19 J) = 5.9622 x 10^-19 J - 3ϕ
- Rearranging the equation, we find: 3ϕ = 3(5.9622 x 10^-19 J) - 5.9622 x 10^-19 J
⇒ 3ϕ = 11.9244 x 10^-19 J - 5.9622 x 10^-19 J
⇒ 3ϕ = 5.9622 x 10^-19 J
⇒ ϕ = (5.9622 x 10^-19 J)/3 ≈
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When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm,the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to:Correct answer is '0.62'. Can you explain this answer?
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When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm,the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to:Correct answer is '0.62'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm,the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to:Correct answer is '0.62'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm,the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to:Correct answer is '0.62'. Can you explain this answer?.
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