Question

An electron is accelerated from rest through a potential difference. After acceleration the electron has a wavelength of 880 nm. What is the potential difference responsible for the acceleration of the electron?

Answer 1

1.95 x 10⁻⁶ volts

Step-by-step explanation:

λ = wavelength of the electron = 880 nm = 880 x 10⁻⁹ m

v = speed of electron = ?

m = mass of electron = 9.1 x 10⁻³¹ kg

Using de-broglie's hyothesis

λ mv = h

(880 x 10⁻⁹) (9.1 x 10⁻³¹) v = 6.63 x 10⁻³⁴

v = 827.92 m/s

ΔV = potential difference responsible for the acceleration of the electron

e = magnitude of charge on electron = 1.6 x 10⁻¹⁹ C

Using conservation of energy

Electric potential energy = Kinetic energy of electron

e ΔV = (0.5) m v²

( 1.6 x 10⁻¹⁹) ΔV = (0.5) (9.1 x 10⁻³¹) (827.92)²

ΔV = 1.95 x 10⁻⁶ volts

Answer 2

`V=1.73* 10^(-6) Volt`

Step-by-step explanation:

We are given that

Initial velocity of electron=0 m/s

Wavelength of electron=880 nm

Wavelength of electron=
`880*10^(-9)`

Where 1 nm =
`10^(-9) m`

We know that

momentum of electron=p=
`(h)/(\lambda)`

Where h=plank's constant =
`6.26* 10^(-34) joule- second`

`\lambda=Wavelength`

Using this formula

`p=(6.26* 10^(-34))/(880* 10^(-9))`

`p=7.1* 10^(-28)`m-seconds

We know that

Kinetic energy in momentum form =potential energy

`(p^2)/(2m)=eV`

Substitute m=
`9.1*10^(-31)Kg,e=1.6* 10^(-19)`

`((7.1* 10^(-28))^2)/(2* 9.1* 10^(-31))=1.6* 10^(-19) V]/tex]</p><p>[tex](50.41* 10^(-56))/(2\cdot9.1* 10^(-31)* 1.6* 10^(-19))=V`

`1.73* 10^(-56+31+19)=V`

`V=1.73* 10^(-6) Volt`

The potential difference responsible for the acceleration of the electron =
`V=1.73* 10^(-6) Volt`