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If the de Broglie wavelength of a particle of mass 'm' is √h times of its velocity then the value of its momentum in terms of its mass (m) and Planck's constant (h) is: (1) √m√h (2)√√mh (3) √m/√h (4) √√h/m?
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If the de Broglie wavelength of a particle of mass 'm' is √h times of ...
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De Broglie Wavelength
The de Broglie wavelength of a particle is given by the formula: λ = h/p, where λ is the de Broglie wavelength, h is Planck's constant, and p is the momentum of the particle.
Given Information
According to the question, the de Broglie wavelength of a particle of mass 'm' is √h times of its velocity. Mathematically, it can be written as λ = √h/v, where v is the velocity of the particle.
Derivation
We know that the momentum of a particle is given by the formula: p = mv, where m is the mass of the particle and v is its velocity. Substituting the given value of λ in the de Broglie wavelength formula, we get:
λ = h/p
√h/v = h/mv
v = mλ/√h
Now, substituting this value of v in the momentum formula, we get:
p = mv
p = m(mλ/√h)
p = √h/m * √mλ
Therefore, the momentum of the particle in terms of its mass and Planck's constant is given by: p = √h/m * √mλ.
Answer
Option (2)√√mh is the correct answer.
De Broglie Wavelength
The de Broglie wavelength of a particle is given by the formula: λ = h/p, where λ is the de Broglie wavelength, h is Planck's constant, and p is the momentum of the particle.
Given Information
According to the question, the de Broglie wavelength of a particle of mass 'm' is √h times of its velocity. Mathematically, it can be written as λ = √h/v, where v is the velocity of the particle.
Derivation
We know that the momentum of a particle is given by the formula: p = mv, where m is the mass of the particle and v is its velocity. Substituting the given value of λ in the de Broglie wavelength formula, we get:
λ = h/p
√h/v = h/mv
v = mλ/√h
Now, substituting this value of v in the momentum formula, we get:
p = mv
p = m(mλ/√h)
p = √h/m * √mλ
Therefore, the momentum of the particle in terms of its mass and Planck's constant is given by: p = √h/m * √mλ.
Answer
Option (2)√√mh is the correct answer.
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If the de Broglie wavelength of a particle of mass 'm' is √h times of its velocity then the value of its momentum in terms of its mass (m) and Planck's constant (h) is: (1) √m√h (2)√√mh (3) √m/√h (4) √√h/m?
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If the de Broglie wavelength of a particle of mass 'm' is √h times of its velocity then the value of its momentum in terms of its mass (m) and Planck's constant (h) is: (1) √m√h (2)√√mh (3) √m/√h (4) √√h/m? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If the de Broglie wavelength of a particle of mass 'm' is √h times of its velocity then the value of its momentum in terms of its mass (m) and Planck's constant (h) is: (1) √m√h (2)√√mh (3) √m/√h (4) √√h/m? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the de Broglie wavelength of a particle of mass 'm' is √h times of its velocity then the value of its momentum in terms of its mass (m) and Planck's constant (h) is: (1) √m√h (2)√√mh (3) √m/√h (4) √√h/m?.
If the de Broglie wavelength of a particle of mass 'm' is √h times of its velocity then the value of its momentum in terms of its mass (m) and Planck's constant (h) is: (1) √m√h (2)√√mh (3) √m/√h (4) √√h/m? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If the de Broglie wavelength of a particle of mass 'm' is √h times of its velocity then the value of its momentum in terms of its mass (m) and Planck's constant (h) is: (1) √m√h (2)√√mh (3) √m/√h (4) √√h/m? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the de Broglie wavelength of a particle of mass 'm' is √h times of its velocity then the value of its momentum in terms of its mass (m) and Planck's constant (h) is: (1) √m√h (2)√√mh (3) √m/√h (4) √√h/m?.
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