An electron mass m with an initial velocity- v -v0 - v0 - 0 is in an electric field- E - E0 - E0- constant -0 - Its de broglie wavelength at time t is given by -0 is the initial wavelength of electron

Let λ_0 = h/mv_0 Force on electron in electric field F = eE = e [ E_0 î ] = e E_0 î Acceleration a = F/m = e E_0 î/m Velocity of the electron after time t , v ...

You visited us 3 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Matter Waves

An electron m...

Question

An electron (mass $m$ ) with an initial velocity, $\to v = v_{0}^i (v_{0} > 0)$ is in an electric field, $\to E = - E_{0}^i (E_{0} = constant > 0)$ . Its de broglie wavelength at time $t$ is given by ( $λ_{0}$ is the initial wavelength of electron)

\frac{λ_{0}}{(1 + \frac{e E_{0}}{m v_{0}} t)}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

λ_{0} (1 + \frac{e E_{0}}{m v_{0}} t)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

λ_{0} t

No worries! We‘ve got your back. Try BYJU‘S free classes today!

λ_{0}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{λ_{0}}{(1 + \frac{e E_{0}}{m v_{0}} t)}$
Let $λ_{0} = \frac{h}{m v_{0}}$
Force on electron in electric field $\to F = - e \to E$
$= - e [- E_{0}^i]$
$= e E_{0}^i$
Acceleration $\to a = \frac{\to F}{m}$
$= \frac{e E_{0}^i}{m}$
Velocity of the electron after time $t$ ,
$\to v = v_{0}^i + (\frac{e E_{0}}{m} t)^i$
$= v_{0} (1 + \frac{e E_{0}}{m v_{0}} t)^i$
$| \to v | = \frac{λ_{0}}{(1 + \frac{e E_{0}}{m v_{0}} t)}$

Suggest Corrections

Similar questions

Q. An electron (mass

m

) with an initial velocity,

\to v = v_{0}^i (v_{0} > 0)

is in an electric field,

\to E = - E_{0}^i (E_{0} = constant > 0)

. Its de broglie wavelength at time

t

is given by (

λ_{0}

is the initial wavelength of electron)

Q. An electron of mass

m

and having an initial velocity

\to v = v_{0}^i (v_{0} > 0)

, enters an electric field

\to E = - E_{0}^i (E_{0} (constant) > 0)

t = 0

. If

λ_{0}

is its de-Broglie wavelength initially, then its de-Broglie wavelength after time

t

is,

Q. An electron of mass m with an initial velocity

\to V = V_{0}^i (V_{0} > 0)

enters an electric field

\to E = - E_{0}^i

(

E_{0} =

constant

> 0

) at

t = 0

. If

λ_{0}

is its de-Broglie wavelength initially, then its de-Broglie wavelength at time t is?

Q. An electron (mass m) with an initial velocity

¯ v = v_{0}^i (v_{0} > 0)

is in an electric field

¯ E = - E_{0}^i

(

E_{0} = c o n s t a n t > 0

). Its de Broglie wavelength at time t is given by

Assume:

(λ_{0} = \frac{h}{m v_{0}})

Q. An electron

(mass m)

with initial velocity

\to v = v_{0}^i + v_{0}^j

is in an electric field

\to E = - E_{0}^k .

λ_{0}

is initial de-Broglie wavelength of electron, its de-Broglie wave length at time

t

is given by

Join BYJU'S Learning Program

An electron (mass m) with an initial velocity, →v=v0 ^i (v0>0) is in an electric field, →E=−E0 ^i (E0=constant>0) . Its de broglie wavelength at time t is given by (λ0 is the initial wavelength of electron)

The correct option is A λ0(1+eE0mv0t)Let λ0=hmv0 Force on electron in electric field →F=−e→E =−e[−E0^i] =eE0^i Acceleration →a=→Fm =eE0^im Velocity of the electron after time t , →v=v0^i+(eE0mt)^i =v0(1+eE0mv0t)^i |→v|=λ0(1+eE0mv0 t)

An electron (mass $m$ ) with an initial velocity, $\to v = v_{0}^i (v_{0} > 0)$ is in an electric field, $\to E = - E_{0}^i (E_{0} = constant > 0)$ . Its de broglie wavelength at time $t$ is given by ( $λ_{0}$ is the initial wavelength of electron)