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Question

(D) The electron enters the region between the plates with an initial kinetic energy of $200 \, eV$.The electric field between the plates is directed

Vedclass · Accepted Answer

None of these

Vedclass · Answer

(D) The electron enters the region between the plates with an initial kinetic energy of $200 \, eV$.The electric field between the plates is directed from the positive plate to the negative plate. Since the electron is negatively charged,it experiences a force opposite to the direction of the electric field,i.e.,it is decelerated.The potential difference between the plates is $V = 100 \, V$,so the work done against the electric field as the electron moves from the first plate to the second plate is $W = qV = 100 \, eV$.The final kinetic energy of the electron when it emerges from the second plate is $K_f = K_i - W = 200 \, eV - 100 \, eV = 100 \, eV$.The de-Broglie wavelength $\lambda$ is given by the formula $\lambda = \frac{12.27}{\sqrt{V}} \, \mathring{A}$,where $V$ is the kinetic energy in electron-volts $(eV)$.Substituting $V = 100 \, eV$,we get $\lambda = \frac{12.27}{\sqrt{100}} = \frac{12.27}{10} = 1.227 \, \mathring{A}$.Rounding to two decimal places,we get $\lambda \approx 1.23 \, \mathring{A}$.Since $1.23 \, \mathring{A}$ is not among the given options,the correct choice is 'None of these'.

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