The E And K relation for a free electron is a parabola A. True B. False
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well this question is incomplete because you didn't mention about E and K .
By the way , if I assume this is related to semiconductor theory .
Then, E is denoted to energy of electrons and k is wave vectors.
Actually, k = 2π/λ
∴ λ = 2π/k
∴Momentum , P = h/λ = h/(2π/k) = hk/2π
Now, Energy of electron , E = P²/2m , here m is mass is electron
∴ E = (hk/2π)²/2m = h²k²/4π²(2m) = h²k²/8π²m
⇒E = h²k²/8π²m
⇒k² = 4(2π²m/h)E
This is in the form of y² = 4ax or x² = 4ay
Hence, the relation between E and K for a free electron is a parabola.
So, option A is correct.
By the way , if I assume this is related to semiconductor theory .
Then, E is denoted to energy of electrons and k is wave vectors.
Actually, k = 2π/λ
∴ λ = 2π/k
∴Momentum , P = h/λ = h/(2π/k) = hk/2π
Now, Energy of electron , E = P²/2m , here m is mass is electron
∴ E = (hk/2π)²/2m = h²k²/4π²(2m) = h²k²/8π²m
⇒E = h²k²/8π²m
⇒k² = 4(2π²m/h)E
This is in the form of y² = 4ax or x² = 4ay
Hence, the relation between E and K for a free electron is a parabola.
So, option A is correct.
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