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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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Given:
- Wavelength of radiation, λ₁ = 500 nm
- Wavelength of radiation, λ₂ = 200 nm
- Maximum kinetic energy of photoelectrons, K₂ = 3K₁
- Work function of the metal = ?
Explanation:
The maximum kinetic energy of photoelectrons can be calculated using the equation:
K.E. = hf - Φ
Where:
- K.E. is the maximum kinetic energy of the photoelectrons
- h is the Planck's constant (6.63 × 10⁻³⁴ J·s)
- f is the frequency of the radiation
- Φ is the work function of the metal
Step 1: Finding the frequency of radiation:
The speed of light, c = λν, where c is the speed of light (3 × 10⁸ m/s), λ is the wavelength, and ν is the frequency of the radiation.
For λ₁ = 500 nm:
ν₁ = c / λ₁
ν₁ = (3 × 10⁸ m/s) / (500 × 10⁻⁹ m)
ν₁ = 6 × 10¹⁴ Hz
For λ₂ = 200 nm:
ν₂ = c / λ₂
ν₂ = (3 × 10⁸ m/s) / (200 × 10⁻⁹ m)
ν₂ = 1.5 × 10¹⁵ Hz
Step 2: Calculating the work function:
Using the equation K.E. = hf - Φ, we can write the equation for K₁ and K₂:
K₁ = hν₁ - Φ
K₂ = hν₂ - Φ
Since K₂ = 3K₁, we can substitute the values:
3K₁ = hν₂ - Φ
Solving for Φ:
Φ = hν₂ - 3K₁
Step 3: Substituting the known values:
Using the given values:
h = 6.63 × 10⁻³⁴ J·s
ν₂ = 1.5 × 10¹⁵ Hz
K₁ = K₂ / 3 = (3K₁) / 3 = K₁
We can substitute these values into the equation for Φ:
Φ = (6.63 × 10⁻³⁴ J·s)(1.5 × 10¹⁵ Hz) - 3K₁
Step 4: Solving for Φ:
Using the given values, we can calculate Φ:
Φ = (9.945 × 10⁻¹⁹ J·s) - 3K₁
We know that Φ is close to 0.62, so:
0.62 = (9.945 × 10⁻¹⁹ J·s) - 3K₁
Solving for K₁:
3K₁ = (9.945 × 10⁻¹⁹ J·s) - 0.62
K₁ = ((9.945 × 10⁻¹⁹ J·s) - 0.62) / 3
K₁ ≈ 3.11 × 10
- Wavelength of radiation, λ₁ = 500 nm
- Wavelength of radiation, λ₂ = 200 nm
- Maximum kinetic energy of photoelectrons, K₂ = 3K₁
- Work function of the metal = ?
Explanation:
The maximum kinetic energy of photoelectrons can be calculated using the equation:
K.E. = hf - Φ
Where:
- K.E. is the maximum kinetic energy of the photoelectrons
- h is the Planck's constant (6.63 × 10⁻³⁴ J·s)
- f is the frequency of the radiation
- Φ is the work function of the metal
Step 1: Finding the frequency of radiation:
The speed of light, c = λν, where c is the speed of light (3 × 10⁸ m/s), λ is the wavelength, and ν is the frequency of the radiation.
For λ₁ = 500 nm:
ν₁ = c / λ₁
ν₁ = (3 × 10⁸ m/s) / (500 × 10⁻⁹ m)
ν₁ = 6 × 10¹⁴ Hz
For λ₂ = 200 nm:
ν₂ = c / λ₂
ν₂ = (3 × 10⁸ m/s) / (200 × 10⁻⁹ m)
ν₂ = 1.5 × 10¹⁵ Hz
Step 2: Calculating the work function:
Using the equation K.E. = hf - Φ, we can write the equation for K₁ and K₂:
K₁ = hν₁ - Φ
K₂ = hν₂ - Φ
Since K₂ = 3K₁, we can substitute the values:
3K₁ = hν₂ - Φ
Solving for Φ:
Φ = hν₂ - 3K₁
Step 3: Substituting the known values:
Using the given values:
h = 6.63 × 10⁻³⁴ J·s
ν₂ = 1.5 × 10¹⁵ Hz
K₁ = K₂ / 3 = (3K₁) / 3 = K₁
We can substitute these values into the equation for Φ:
Φ = (6.63 × 10⁻³⁴ J·s)(1.5 × 10¹⁵ Hz) - 3K₁
Step 4: Solving for Φ:
Using the given values, we can calculate Φ:
Φ = (9.945 × 10⁻¹⁹ J·s) - 3K₁
We know that Φ is close to 0.62, so:
0.62 = (9.945 × 10⁻¹⁹ J·s) - 3K₁
Solving for K₁:
3K₁ = (9.945 × 10⁻¹⁹ J·s) - 0.62
K₁ = ((9.945 × 10⁻¹⁹ J·s) - 0.62) / 3
K₁ ≈ 3.11 × 10
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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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