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For a proton to capture an electron to form a neutron and a neutrino (assumed massless), the electron must have some minimum energy. For such an electron the de Broglie wavelength in picometers is ______.
(Specify your answer to two digits after the decimal point.)
Correct answer is between '1.00,1.10'. Can you explain this answer?
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For a proton to capture an electron to form a neutron and a neutrino (...
**De Broglie wavelength**
The de Broglie wavelength is a concept in quantum mechanics that describes the wave-like properties of particles. It is given by the equation:
λ = h / p
Where:
- λ is the de Broglie wavelength
- h is the Planck's constant (6.626 x 10^-34 J s)
- p is the momentum of the particle
The de Broglie wavelength can be used to determine the minimum energy required for an electron to be captured by a proton and form a neutron and a neutrino.
**Minimum energy for electron capture**
In this process, a proton captures an electron to form a neutron and a neutrino. The energy required for this process can be calculated using the conservation of energy principle.
The initial energy of the system is the sum of the kinetic energy of the electron and the rest energy of the proton. The final energy of the system is the sum of the kinetic energy of the neutron and the neutrino.
Since the neutrino is assumed to be massless, its kinetic energy is zero. Therefore, the final energy is equal to the kinetic energy of the neutron.
For the electron to be captured, its kinetic energy must be greater than the difference in energy between the initial and final states.
**Calculating the de Broglie wavelength**
To calculate the de Broglie wavelength of the electron, we need to determine its momentum. The momentum of an electron can be calculated using the equation:
p = √(2mE)
Where:
- p is the momentum
- m is the mass of the electron (9.109 x 10^-31 kg)
- E is the kinetic energy of the electron
Substituting the value of momentum into the de Broglie wavelength equation, we can calculate the wavelength.
Since the question asks for the de Broglie wavelength in picometers (pm), we need to convert the wavelength from meters to picometers by multiplying by 10^12.
The correct answer is between 1.00 pm and 1.10 pm, which represents the minimum energy required for the electron to be captured by the proton and form a neutron and a neutrino.
The de Broglie wavelength is a concept in quantum mechanics that describes the wave-like properties of particles. It is given by the equation:
λ = h / p
Where:
- λ is the de Broglie wavelength
- h is the Planck's constant (6.626 x 10^-34 J s)
- p is the momentum of the particle
The de Broglie wavelength can be used to determine the minimum energy required for an electron to be captured by a proton and form a neutron and a neutrino.
**Minimum energy for electron capture**
In this process, a proton captures an electron to form a neutron and a neutrino. The energy required for this process can be calculated using the conservation of energy principle.
The initial energy of the system is the sum of the kinetic energy of the electron and the rest energy of the proton. The final energy of the system is the sum of the kinetic energy of the neutron and the neutrino.
Since the neutrino is assumed to be massless, its kinetic energy is zero. Therefore, the final energy is equal to the kinetic energy of the neutron.
For the electron to be captured, its kinetic energy must be greater than the difference in energy between the initial and final states.
**Calculating the de Broglie wavelength**
To calculate the de Broglie wavelength of the electron, we need to determine its momentum. The momentum of an electron can be calculated using the equation:
p = √(2mE)
Where:
- p is the momentum
- m is the mass of the electron (9.109 x 10^-31 kg)
- E is the kinetic energy of the electron
Substituting the value of momentum into the de Broglie wavelength equation, we can calculate the wavelength.
Since the question asks for the de Broglie wavelength in picometers (pm), we need to convert the wavelength from meters to picometers by multiplying by 10^12.
The correct answer is between 1.00 pm and 1.10 pm, which represents the minimum energy required for the electron to be captured by the proton and form a neutron and a neutrino.
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For a proton to capture an electron to form a neutron and a neutrino (assumed massless), the electron must have some minimum energy. For such an electron the de Broglie wavelength in picometers is ______.(Specify your answer to two digits after the decimal point.)Correct answer is between '1.00,1.10'. Can you explain this answer?
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For a proton to capture an electron to form a neutron and a neutrino (assumed massless), the electron must have some minimum energy. For such an electron the de Broglie wavelength in picometers is ______.(Specify your answer to two digits after the decimal point.)Correct answer is between '1.00,1.10'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about For a proton to capture an electron to form a neutron and a neutrino (assumed massless), the electron must have some minimum energy. For such an electron the de Broglie wavelength in picometers is ______.(Specify your answer to two digits after the decimal point.)Correct answer is between '1.00,1.10'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a proton to capture an electron to form a neutron and a neutrino (assumed massless), the electron must have some minimum energy. For such an electron the de Broglie wavelength in picometers is ______.(Specify your answer to two digits after the decimal point.)Correct answer is between '1.00,1.10'. Can you explain this answer?.
For a proton to capture an electron to form a neutron and a neutrino (assumed massless), the electron must have some minimum energy. For such an electron the de Broglie wavelength in picometers is ______.(Specify your answer to two digits after the decimal point.)Correct answer is between '1.00,1.10'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about For a proton to capture an electron to form a neutron and a neutrino (assumed massless), the electron must have some minimum energy. For such an electron the de Broglie wavelength in picometers is ______.(Specify your answer to two digits after the decimal point.)Correct answer is between '1.00,1.10'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a proton to capture an electron to form a neutron and a neutrino (assumed massless), the electron must have some minimum energy. For such an electron the de Broglie wavelength in picometers is ______.(Specify your answer to two digits after the decimal point.)Correct answer is between '1.00,1.10'. Can you explain this answer?.
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