Question

An electron of mass m and 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 ______.

पर्याय

• `(-"h")/("eEt"^2)`

• `(-"eht")/"E"`

• `(-"mh")/("eEt"^2)`

• `(-"h")/("eE")`

Answer 1

An electron of mass m and 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 `underlinebb((-"h")/("eEt"^2))`.

Explanation:

Here, u = 0; a = `"eE"/"m"`; v = ?; t = t

∴ v = u + at = 0 + `"eE"/"m""t"`

de-Broglie wavelength,

λ = `"h"/"mv"="h"/("m"("eEt"//"m"))="h"/"eEt"`

Rate of change of de-Broglie wavelength

`("d"lambda)/"dt"="h"/"eE"(-1/"t"^2)=-"h"/"eEt"^2`