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 :

Question

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 : (A) (-h/|e|Et2) (B) (|e|Et/h) (C) -(h/|e|Et) (D) -(h/|e|E√t)

Tardigrade Admin · Accepted Answer

a = (eE/m) v = u+at =((eE/m))t λ = (h/mv) (dλ/dt) = (-(hm). (dv/dt)/(mv)2) = -(ah/mv2) = -(h/|e|Et2)

Q. 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 :

$\frac{- h}{∣ e ∣ E t ^{2}}$

$\frac{∣ e ∣ Et}{h}$

$- \frac{h}{∣ e ∣ Et}$

$- \frac{h}{∣ e ∣ E t}$

$a = \frac{e E}{m}$
$v = u + a t = (\frac{e E}{m}) t$
$λ = \frac{h}{m v}$
$\frac{d λ}{d t} = \frac{- ( hm ) . \frac{d v}{d t}}{( m v ) ^{2}} = - \frac{ah}{m v ^{2}} = - \frac{h}{∣ e ∣ E t ^{2}}$

Q. 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 :

∣e∣Et2−h​

h∣e∣Et​

−∣e∣Eth​

−∣e∣Et​h​