An electron mass m with an initial velocity- v -v0 - v0 - 0 is in an electric field- E - E0 - E0- constant -0 - Its de broglie wavelength at time t is given by -0 is the initial wavelength of electron

Let λ_0 = h/mv_0 Force on electron in electric field F = eE = e [ E_0 î ] = e E_0 î Acceleration a = F/m = e E_0 î/m Velocity of the electron after time t , v ...

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Standard XII

Physics

Matter Waves

An electron m...

Question

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

\frac{λ_{0}}{(1 + \frac{e E_{0}}{m v_{0}} t)}

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λ_{0} (1 + \frac{e E_{0}}{m v_{0}} t)

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λ_{0} t

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λ_{0}

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Solution

The correct option is A $\frac{λ_{0}}{(1 + \frac{e E_{0}}{m v_{0}} t)}$
Let $λ_{0} = \frac{h}{m v_{0}}$
Force on electron in electric field $\to F = - e \to E$
$= - e [- E_{0}^i]$
$= e E_{0}^i$
Acceleration $\to a = \frac{\to F}{m}$
$= \frac{e E_{0}^i}{m}$
Velocity of the electron after time $t$ ,
$\to v = v_{0}^i + (\frac{e E_{0}}{m} t)^i$
$= v_{0} (1 + \frac{e E_{0}}{m v_{0}} t)^i$
$| \to v | = \frac{λ_{0}}{(1 + \frac{e E_{0}}{m v_{0}} t)}$

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An electron (mass m) with an initial velocity, →v=v0 ^i (v0>0) is in an electric field, →E=−E0 ^i (E0=constant>0) . Its de broglie wavelength at time t is given by (λ0 is the initial wavelength of electron)

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