An electron, an alpha particle and a proton has the same photon. Which one has the shortest wavelength?
Answers
Explanation:
In this case, protons are heavier compared to electrons, and alpha particles are composed of two protons. Hence the alpha particle is the heaviest compared to a proton and an electron. Therefore, the alpha particle has the shortest wavelength. Therefore, the alpha particle has the shortest wavelength.
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The alpha particle has the shortest wavelength.
Explanation:
Given:
An electron, an alpha particle, and a proton has the same kinetic energy.
The mass of the electron m e = 9.1 × 10 ^− 31 kg
The mass of the proton m p = 1.67 × 10 ^− 27 kg
The mass of the alpha particle m α = 4 × m p = 6.68 × 10^ − 27 kg
Now recall that the De Broglie wavelength is computed as:
⇒ λ = h / √ 2 m K
The particles have the same kinetic energy So:
⇒ λ ∝ 1 /√ m
The wavelength is inversely proportional to the square root of the mass. Thus the particle with higher mass has the shortest wavelength.
In this case, protons are heavier compared to electrons, and alpha particles are composed of two protons. Hence the alpha particle is the heaviest compared to a proton and an electron.