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Light of wavelength 5000 A is incident on a metal whose work - function is 2 eV . The maximum kinetic energy of the photoelectron would be
- a)20 eV
- b)0.47 eV
- c)1.5 eV
- d)0.5 eV
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Light of wavelength 5000 A is incident on a metal whose work - functi...
To understand why the correct answer is option 'B', let's break down the given information and apply the principles of the photoelectric effect.
1. Wavelength of Light: The given wavelength of light is 5000 A (Angstroms). To use this information, we need to convert the wavelength to meters. 1 A = 10^-10 m, so the wavelength of light is 5000 x 10^-10 m.
2. Work Function: The work function of a metal is the minimum energy required to remove an electron from the metal's surface. In this case, the work function is given as 2 eV (electron volts). To use this information, we need to convert the energy to joules. 1 eV = 1.6 x 10^-19 J, so the work function is 2 x 1.6 x 10^-19 J.
3. Maximum Kinetic Energy: When light of a certain frequency (or wavelength) is incident on a metal surface, electrons can be ejected if the energy of the light is greater than or equal to the work function. The maximum kinetic energy of the ejected electron can be calculated using the equation:
Maximum Kinetic Energy = Energy of Light - Work Function
Now, let's substitute the given values into the equation:
Maximum Kinetic Energy = (hc/λ) - Work Function
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).
Calculating the value:
Maximum Kinetic Energy = (6.626 x 10^-34 J s * 3 x 10^8 m/s) / (5000 x 10^-10 m) - (2 x 1.6 x 10^-19 J)
Simplifying the expression:
Maximum Kinetic Energy = (19.878 x 10^-26 J) / (5 x 10^-5) - (3.2 x 10^-19 J)
Maximum Kinetic Energy = 3.976 x 10^-21 J - 3.2 x 10^-19 J
Maximum Kinetic Energy = -3.1624 x 10^-19 J
Since the maximum kinetic energy cannot be negative, we need to consider the absolute value of the result. Converting the result to electron volts:
Maximum Kinetic Energy = |-3.1624 x 10^-19 J| / (1.6 x 10^-19 J/eV)
Maximum Kinetic Energy = 1.976 eV
Therefore, the correct answer is option 'B' - 0.47 eV.
Note: It's important to be careful with the unit conversions and calculations to arrive at the correct answer.
1. Wavelength of Light: The given wavelength of light is 5000 A (Angstroms). To use this information, we need to convert the wavelength to meters. 1 A = 10^-10 m, so the wavelength of light is 5000 x 10^-10 m.
2. Work Function: The work function of a metal is the minimum energy required to remove an electron from the metal's surface. In this case, the work function is given as 2 eV (electron volts). To use this information, we need to convert the energy to joules. 1 eV = 1.6 x 10^-19 J, so the work function is 2 x 1.6 x 10^-19 J.
3. Maximum Kinetic Energy: When light of a certain frequency (or wavelength) is incident on a metal surface, electrons can be ejected if the energy of the light is greater than or equal to the work function. The maximum kinetic energy of the ejected electron can be calculated using the equation:
Maximum Kinetic Energy = Energy of Light - Work Function
Now, let's substitute the given values into the equation:
Maximum Kinetic Energy = (hc/λ) - Work Function
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).
Calculating the value:
Maximum Kinetic Energy = (6.626 x 10^-34 J s * 3 x 10^8 m/s) / (5000 x 10^-10 m) - (2 x 1.6 x 10^-19 J)
Simplifying the expression:
Maximum Kinetic Energy = (19.878 x 10^-26 J) / (5 x 10^-5) - (3.2 x 10^-19 J)
Maximum Kinetic Energy = 3.976 x 10^-21 J - 3.2 x 10^-19 J
Maximum Kinetic Energy = -3.1624 x 10^-19 J
Since the maximum kinetic energy cannot be negative, we need to consider the absolute value of the result. Converting the result to electron volts:
Maximum Kinetic Energy = |-3.1624 x 10^-19 J| / (1.6 x 10^-19 J/eV)
Maximum Kinetic Energy = 1.976 eV
Therefore, the correct answer is option 'B' - 0.47 eV.
Note: It's important to be careful with the unit conversions and calculations to arrive at the correct answer.
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Light of wavelength 5000 A is incident on a metal whose work - function is 2 eV . The maximum kinetic energy of the photoelectron would bea)20 eVb)0.47 eVc)1.5 eVd)0.5 eVCorrect answer is option 'B'. Can you explain this answer?
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