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The debroglie wavelength of a particle moving with a velocity 2.25 ×10 raised to8 is eqal to that of a photon. The ratio of theri kinetic energies is.?
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De Broglie Wavelength Comparison
The de Broglie wavelength is given by the formula λ = h / p, where λ is the wavelength, h is the Planck constant, and p is the momentum of the particle.
Given Information
- Velocity of the particle = 2.25 × 10^8 m/s
- Ratio of de Broglie wavelength to that of a photon = 1
Calculating the de Broglie Wavelength
- The momentum of a particle is given by p = mv, where m is the mass of the particle and v is its velocity.
- Let's assume the mass of the particle is m.
- Therefore, the de Broglie wavelength of the particle is λ = h / (m * v).
Comparing with Photon
- The de Broglie wavelength of a photon is given by λ = c / f, where c is the speed of light and f is the frequency of the photon.
- Since the ratio of their wavelengths is given as 1, we have:
h / (m * v) = c / f
f = (m * v * c) / h
Calculating the Ratio of Kinetic Energies
- The kinetic energy of a particle is given by KE = 0.5 * m * v^2.
- The kinetic energy of a photon is given by KE = hf, where h is the Planck constant.
- Therefore, the ratio of their kinetic energies is:
KE_particle / KE_photon = (0.5 * m * v^2) / (h * f)
= (0.5 * m * v^2) / (m * v * c)
= 0.5 * v / c
Conclusion
The ratio of the kinetic energies of the particle and the photon moving with the given velocity is 0.5 * v / c.
The de Broglie wavelength is given by the formula λ = h / p, where λ is the wavelength, h is the Planck constant, and p is the momentum of the particle.
Given Information
- Velocity of the particle = 2.25 × 10^8 m/s
- Ratio of de Broglie wavelength to that of a photon = 1
Calculating the de Broglie Wavelength
- The momentum of a particle is given by p = mv, where m is the mass of the particle and v is its velocity.
- Let's assume the mass of the particle is m.
- Therefore, the de Broglie wavelength of the particle is λ = h / (m * v).
Comparing with Photon
- The de Broglie wavelength of a photon is given by λ = c / f, where c is the speed of light and f is the frequency of the photon.
- Since the ratio of their wavelengths is given as 1, we have:
h / (m * v) = c / f
f = (m * v * c) / h
Calculating the Ratio of Kinetic Energies
- The kinetic energy of a particle is given by KE = 0.5 * m * v^2.
- The kinetic energy of a photon is given by KE = hf, where h is the Planck constant.
- Therefore, the ratio of their kinetic energies is:
KE_particle / KE_photon = (0.5 * m * v^2) / (h * f)
= (0.5 * m * v^2) / (m * v * c)
= 0.5 * v / c
Conclusion
The ratio of the kinetic energies of the particle and the photon moving with the given velocity is 0.5 * v / c.
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The debroglie wavelength of a particle moving with a velocity 2.25 ×10 raised to8 is eqal to that of a photon. The ratio of theri kinetic energies is.?
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The debroglie wavelength of a particle moving with a velocity 2.25 ×10 raised to8 is eqal to that of a photon. The ratio of theri kinetic energies is.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The debroglie wavelength of a particle moving with a velocity 2.25 ×10 raised to8 is eqal to that of a photon. The ratio of theri kinetic energies is.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The debroglie wavelength of a particle moving with a velocity 2.25 ×10 raised to8 is eqal to that of a photon. The ratio of theri kinetic energies is.?.
The debroglie wavelength of a particle moving with a velocity 2.25 ×10 raised to8 is eqal to that of a photon. The ratio of theri kinetic energies is.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The debroglie wavelength of a particle moving with a velocity 2.25 ×10 raised to8 is eqal to that of a photon. The ratio of theri kinetic energies is.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The debroglie wavelength of a particle moving with a velocity 2.25 ×10 raised to8 is eqal to that of a photon. The ratio of theri kinetic energies is.?.
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