Question

The de Broglie wavelength of an electron accelerated through a p.d.V is directly proportional to V'' .Then n must be equal to (n=) (a) 1 (b)-1 (c) 0.5 (d) -0.5​

Answer 1

Given info : The De-Broglie's wavelength of an electron accelerated through a potential difference V is directly proportional to Vⁿ.

To find : value of n must be equal to ..

solution : let charge on electron is e

then electric potential energy of electron = eV

from conservation of energy theorem,

kinetic energy of electron, K = electric potential energy = eV

⇒K = eV

but Kinetic energy , K = P²/2m , P is linear momentum and m is mass of electron.

so, eV = P²/2m

⇒2meV = P²

⇒P = √(2meV)

From De-Broglie's wavelength equation,

λ = h/p = h/√(2meV)

⇒λ = h/√(2me) × V¯(¹/²)

⇒λ ∝ V^(-0.5)

Therefore the value of n is -0.5.

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