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Calculate the de Broglie wavelength for an electron with momentum 8.00×10⁻²⁴ kgms ⁻¹ and determine the energy of the electron.

User Vmenezes
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Final answer:

To calculate the de Broglie wavelength of an electron with a given momentum, you can use the formula λ = h / p, where λ is the de Broglie wavelength, h is Planck's constant, and p is the momentum. Substituting the given values into the formula, we find that the de Broglie wavelength is approximately 8.28 x 10^-8 meters. To determine the energy of the electron, you can use the formula E = (p^2) / (2m), where E is the energy, p is the momentum, and m is the mass of the electron. Substituting the given values into the formula, we find that the energy of the electron is approximately 2.70 x 10^-13 joules.

Step-by-step explanation:

To calculate the de Broglie wavelength of an electron, you can use the formula:



λ = h / p



Where λ is the de Broglie wavelength, h is the Planck's constant (6.626 x 10^-34 Js), and p is the momentum of the electron.



Substituting the given momentum (8.00×10¹zkgms¹z) into the formula, we get:



λ = (6.626 x 10^-34 Js) / (8.00×10¹z kgms¹z)



Simplifying the calculation, we find that the de Broglie wavelength is approximately [b]8.28 x 10^-8 meters[/b].



To determine the energy of the electron, you can use the formula:



E = (p^2) / (2m)



Where E is the energy, p is the momentum of the electron, and m is the mass of the electron.



Substituting the given momentum (8.00×10¹z kgms¹z) and the mass of an electron (9.11 x 10^-31 kg) into the formula, we get:



E = ((8.00×10¹z kgms¹z)^2) / (2 × 9.11 x 10^-31 kg)



Simplifying the calculation, we find that the energy of the electron is approximately [b]2.70 x 10^-13 joules[/b].

User Lyjackal
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