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Photons of energy 1eV and 2.5 eV successively illuminate a metal whose work function is 0.5 eV. The ratio of the maximum speeds of the electrons emitted will be
- a)1 : 4
- b)1 : 2
- c)2 : 1
- d)4 : 1
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Photons of energy 1eV and 2.5 eV successively illuminate a metal whose...
Explanation:
To solve this problem, we need to apply the concept of the photoelectric effect and use the equation for kinetic energy.
Photoelectric Effect:
The photoelectric effect is the phenomenon where electrons are emitted from a material when it is illuminated with light of sufficient energy. The energy of the incident photons determines the maximum kinetic energy of the emitted electrons.
Equation for Kinetic Energy:
The equation for kinetic energy is given by:
K.E. = (1/2)mv²
Where:
K.E. is the kinetic energy of the electron
m is the mass of the electron
v is the velocity of the electron
Work Function:
The work function (φ) of a material is the minimum amount of energy required to remove an electron from the material.
Application to the Problem:
Given:
Photon 1 energy (E₁) = 1 eV
Photon 2 energy (E₂) = 2.5 eV
Work function (φ) = 0.5 eV
We need to find the ratio of the maximum speeds of the emitted electrons.
Step 1: Calculate the Maximum Kinetic Energy:
The maximum kinetic energy of the emitted electrons can be calculated using the difference between the energy of the incident photons and the work function:
K.E. = E - φ
For Photon 1:
K.E₁ = E₁ - φ = 1 eV - 0.5 eV = 0.5 eV
For Photon 2:
K.E₂ = E₂ - φ = 2.5 eV - 0.5 eV = 2 eV
Step 2: Calculate the Maximum Speed:
To calculate the maximum speed of the electrons, we can equate the kinetic energy to the equation for kinetic energy:
K.E. = (1/2)mv²
For Photon 1:
0.5 eV = (1/2)mv₁²
For Photon 2:
2 eV = (1/2)mv₂²
Step 3: Find the Ratio of Maximum Speeds:
To find the ratio of the maximum speeds, we can divide the equation for Photon 2 by the equation for Photon 1:
(2 eV) / (0.5 eV) = ((1/2)mv₂²) / ((1/2)mv₁²)
Simplifying the equation:
4 = (v₂²) / (v₁²)
Taking the square root of both sides:
2 = v₂ / v₁
Therefore, the ratio of the maximum speeds of the emitted electrons is 1:2, which corresponds to option B.
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Photons of energy 1eV and 2.5 eV successively illuminate a metal whose work function is 0.5 eV. The ratio of the maximum speeds of the electrons emitted will bea)1 : 4b)1 : 2c)2 : 1d)4 : 1Correct answer is option 'B'. Can you explain this answer?
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