Answer:
[tex]V=1.73\times 10^{-6} Volt[/tex]
Explanation:
We are given that
Initial velocity of electron=0 m/s
Wavelength of electron=880 nm
Wavelength of electron=[tex]880\times10^{-9}[/tex]
Where 1 nm =[tex]10^{-9} m[/tex]
We know that
momentum of electron=p= [tex]\frac{h}{\lambda}[/tex]
Where h=plank's constant =[tex]6.26\times 10^{-34} joule- second[/tex]
[tex]\lambda=Wavelength[/tex]
Using this formula
[tex]p=\frac{6.26\times 10^{-34}}{880\times 10^{-9}}[/tex]
[tex]p=7.1\times 10^{-28}[/tex]m-seconds
We know that
Kinetic energy in momentum form =potential energy
[tex]\frac{p^2}{2m}=eV[/tex]
Substitute m=[tex]9.1\times10^{-31}Kg,e=1.6\times 10^{-19}[/tex]
[tex]\frac{(7.1\times 10^{-28})^2}{2\times 9.1\times 10^{-31}}=1.6\times 10^{-19} V]/tex]
[tex]\frac{50.41\times 10^{-56}}{2\cdot9.1\times 10^{-31}\times 1.6\times 10^{-19}}=V[/tex]
[tex]1.73\times 10^{-56+31+19}=V[/tex]
[tex]V=1.73\times 10^{-6} Volt[/tex]
The potential difference responsible for the acceleration of the electron =[tex]V=1.73\times 10^{-6} Volt[/tex]
Answer:
1.95 x 10⁻⁶ volts
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
