Compare wavelength of electron and photon having same energy
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Answered by
7
hell. ooo
If two particles have the same de Broglie wavelength, they have the same momentum:
λ=hpλ=hp
From relativity, we know that E2=(mc2)2+(pc)2E2=(mc2)2+(pc)2.
Therefore, the proton will have a higher energy due to its higher rest mass.
hope this helps you. !!
If two particles have the same de Broglie wavelength, they have the same momentum:
λ=hpλ=hp
From relativity, we know that E2=(mc2)2+(pc)2E2=(mc2)2+(pc)2.
Therefore, the proton will have a higher energy due to its higher rest mass.
hope this helps you. !!
Answered by
23
Energy of electron
E₁ = p² / (2m)
= (h/λ)² / (2m)
= h² / (2mλ₁²)
Energy of photon
E₂ = hc / λ₂
If E₁ = E₂
h² / (2mλ₁²) = hc / λ₂
λ₁² = λ₂h / (2mc)
λ₁² = λ₂ × (6.626 × 10^-34 / (2 × 9.1 × 10^-31))
λ₁² = λ₂ × 0.000364
λ₂ = 2746.7 × λ₁²
From above we can say that
Wavelength of photon is longer than that of electron.
E₁ = p² / (2m)
= (h/λ)² / (2m)
= h² / (2mλ₁²)
Energy of photon
E₂ = hc / λ₂
If E₁ = E₂
h² / (2mλ₁²) = hc / λ₂
λ₁² = λ₂h / (2mc)
λ₁² = λ₂ × (6.626 × 10^-34 / (2 × 9.1 × 10^-31))
λ₁² = λ₂ × 0.000364
λ₂ = 2746.7 × λ₁²
From above we can say that
Wavelength of photon is longer than that of electron.
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