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Standard XII

Physics

Potential Energy - External Viewpoint

A charge part...

Question

A charge particle $q_{0}$ of mass $m_{0}$ is projected along the y-axis at $t = 0$ from origin with a velocity $V_{0} .$ If a uniform electric field $E_{0}$ also exists along the x-axis, then the time at which de Broglie wavelength of the particle becomes half of the initial value is :

\frac{m_{0} v_{0}}{q_{0} E_{0}}

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2 \frac{m_{0} v_{0}}{q_{0} E_{0}}

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\sqrt{3} \frac{m_{0} v_{0}}{q_{0} E_{0}}

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3 \frac{m_{0} v_{0}}{q_{0} E_{0}}

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Solution

The correct option is C $\sqrt{3} \frac{m_{0} v_{0}}{q_{0} E_{0}}$
Initial debrogle wavelength of the charge particle $λ_{0} = \frac{h}{m_{0} v_{0}}$
After any time t, $λ^{'} = \frac{h}{m_{0} \sqrt{V_{0}^{2} + {(\frac{q E_{0} t}{m_{0}})}^{2}}}$
Suppose after time t, $λ$ becomes half of the initial value i.e. $λ = λ_{0} / 2$ .
$t = \sqrt{3} \frac{m_{0} v_{0}}{q_{0} E_{0}}$

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A charge particle q0 of mass m0 is projected along the y-axis at t=0 from origin with a velocity V0. If a uniform electric field E0 also exists along the x-axis, then the time at which de Broglie wavelength of the particle becomes half of the initial value is :

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A charge particle $q_{0}$ of mass $m_{0}$ is projected along the y-axis at $t = 0$ from origin with a velocity $V_{0} .$ If a uniform electric field $E_{0}$ also exists along the x-axis, then the time at which de Broglie wavelength of the particle becomes half of the initial value is :