JEE MAIN - Physics (2020 - 9th January Evening Slot - No. 6)
An electron of mass m and magnitude of charge
|e| initially at rest gets accelerated by a constant
electric field E. The rate of change of de-Broglie
wavelength of this electron at time t ignoring
relativistic effects is :
$${{ - h} \over {\left| e \right|Et}}$$
$${{ - h} \over {\left| e \right|E\sqrt t }}$$
$${{ - h} \over {\left| e \right|E{t^2}}}$$
$${{\left| e \right|Et} \over h}$$
Explanation
F = |e| E
$$a = {F \over m}$$ = $${{\left| e \right|E} \over m}$$
V = $$at = $$ $${{\left| e \right|E} \over m}t$$
$$\lambda $$ = $${h \over {mV}}$$ = $${h \over {\left| e \right|Et}}$$
$${{d\lambda } \over {dt}}$$ = $${{ - h} \over {\left| e \right|E{t^2}}}$$
$$a = {F \over m}$$ = $${{\left| e \right|E} \over m}$$
V = $$at = $$ $${{\left| e \right|E} \over m}t$$
$$\lambda $$ = $${h \over {mV}}$$ = $${h \over {\left| e \right|Et}}$$
$${{d\lambda } \over {dt}}$$ = $${{ - h} \over {\left| e \right|E{t^2}}}$$
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