An electron (mass m) with an initial velocity v = v 0 i ^ ( v 0 > 0 ) is in an electric field E = − E 0 i ^ ( E 0 = constant > 0 ). Its de Broglie wavelength at time t is given by

Force on the electron = − e E = + e E 0 i ^ , so v = v 0 + m e E 0 t . λ = m v h = 1 + m v 0 e E 0 t λ 0 .

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PhysicsModern PhysicsDe Broglie & Matter WavesMedium2 minQB

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An electron (mass m) with an initial velocity $v = v_{0} \hat{i} (v_{0} > 0)$ is in an electric field $E = - E_{0} \hat{i} (E_{0}$ = constant $> 0$ ). Its de Broglie wavelength at time t is given by

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Solution:

Force on the electron $= - e E = + e E_{0} \hat{i}$ , so $v = v_{0} + \frac{e E _{0} t}{m}$ .

$λ = \frac{h}{m v} = \frac{λ _{0}}{1 + \frac{e E _{0} t}{m v _{0}}} .$

Subject:PhysicsTopic:Modern PhysicsSubtopic:De Broglie & Matter Waves

⏱ 2mℹ️ Source: QB

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