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Calculate the wavelength of an electron that has been accelerated in a particle accelerator through potential difference of hundred million volts?
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Calculate the wavelength of an electron that has been accelerated in a...
Calculation of Wavelength of an Electron Accelerated through Potential Difference of 100 Million Volts
Explanation
When an electron is accelerated through a potential difference, it gains kinetic energy, which can be calculated using the formula:
Kinetic Energy (K) = qV
where q is the charge of the electron and V is the potential difference.
The de Broglie wavelength of the electron can be calculated using the formula:
λ = h/p
where λ is the wavelength, h is Planck's constant, and p is the momentum of the electron.
The momentum of the electron can be calculated using the formula:
p = sqrt(2mK)
where m is the mass of the electron.
Calculation
Given that the potential difference is 100 million volts, the kinetic energy gained by the electron can be calculated as:
K = (1.6 x 10^-19 C) x (100 x 10^6 V) = 1.6 x 10^-12 J
The momentum of the electron can be calculated as:
p = sqrt(2 x (9.11 x 10^-31 kg) x (1.6 x 10^-12 J)) = 1.825 x 10^-21 kg m/s
Finally, the de Broglie wavelength of the electron can be calculated as:
λ = (6.626 x 10^-34 J s) / (1.825 x 10^-21 kg m/s) = 3.63 x 10^-13 m
Therefore, the wavelength of the electron accelerated through a potential difference of 100 million volts is 3.63 x 10^-13 meters.
Community Answer
Calculate the wavelength of an electron that has been accelerated in a...
Energy =qv
where q= charge on electron
v= potential difference
now wavelength = h/√2mqv
calculate the wavelength
m is mass of electron
where q= charge on electron
v= potential difference
now wavelength = h/√2mqv
calculate the wavelength
m is mass of electron
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Calculate the wavelength of an electron that has been accelerated in a particle accelerator through potential difference of hundred million volts?
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Calculate the wavelength of an electron that has been accelerated in a particle accelerator through potential difference of hundred million volts? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Calculate the wavelength of an electron that has been accelerated in a particle accelerator through potential difference of hundred million volts? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the wavelength of an electron that has been accelerated in a particle accelerator through potential difference of hundred million volts?.
Calculate the wavelength of an electron that has been accelerated in a particle accelerator through potential difference of hundred million volts? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Calculate the wavelength of an electron that has been accelerated in a particle accelerator through potential difference of hundred million volts? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the wavelength of an electron that has been accelerated in a particle accelerator through potential difference of hundred million volts?.
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