How different are the de Broglie wavelengths of a proton and

What is the difference in de Broglie wavelengths for a proton and a hydrogen atom moving with the same kinetic energy T = 1 eV?

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Item name: De Broglie wavelengths of proton and hydrogen atom

Product Description: Want to know about the difference in de Broglie wavelengths for a proton and a hydrogen atom? Our digital product provides detailed information on this issue. You will gain access to up-to-date data and scientific research that will help you better understand physical laws and phenomena.

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• Format: PDF
• Russian language
• Number of pages: 10
• File size: 1.5 MB

Price: 150 rubles

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Our digital product code #DB-457 provides a detailed description of the difference in de Broglie wavelengths for a proton and a hydrogen atom moving with the same kinetic energy T = 1 eV. The PDF file in Russian contains 10 pages of up-to-date data and scientific research that will help you better understand physical laws and phenomena.

Technical characteristics of the product: format - PDF, language - Russian, number of pages - 10, file size - 1.5 MB, price - 150 rubles.

After payment, you will be able to download a file with a detailed solution to problem 60528, which contains a brief record of the conditions, formulas and laws used in the solution, the derivation of the calculation formula and the answer. The file is presented in image format.

If you have any questions about the solution, our managers are always ready to help you and provide the necessary information support. You can buy this product by adding it to your cart and placing an order on our website.

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The de Broglie wavelength for a particle is calculated by the formula λ = h/p, where h is Planck’s constant, p is the momentum of the particle. For a proton with an energy of 1 eV, the momentum will be equal to p = √(2mT), where m is the mass of the proton, T is the kinetic energy. For a hydrogen atom with the same kinetic energy, the momentum will be equal to p = √(2μT), where μ is the reduced mass of the proton-electron system. Since the mass of an electron is much less than the mass of a proton, μ is approximately equal to the mass of the electron. Thus, for a proton and a hydrogen atom with the same kinetic energy, the de Broglie wavelengths will differ by approximately √(mp/me) times, where mp is the mass of the proton, me is the mass of the electron.

To accurately solve the problem, it is necessary to know the exact masses of the proton and electron, which are approximately 1.0073 atomic units and 0.00054858 atomic units, respectively. Substituting these values, we find that the ratio of the de Broglie wavelengths of a proton and a hydrogen atom with the same kinetic energy will be approximately equal to √(1836), that is, approximately 42.8.

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