Respuesta :
Answer:
The speed of electron is [tex]3.2\times10^{6}\ m/s[/tex]
Explanation:
Given that,
Energy density = 0.1 J/m³
Separation = 0.2 mm
We need to calculate the potential difference
Using formula of energy density
[tex]J=\dfrac{1}{2}\epsilon_{0}E^2[/tex]
[tex]J=\dfrac{1}{2}\epsilon_{0}\dfrac{V^2}{d^2}[/tex]
[tex]V^2=\dfrac{0.1\times(0.2\times10^{-3})^2\times2}{8.85\times10^{-12}}[/tex]
[tex]V^2=\sqrt{903.95}[/tex]
[tex]V=30.06\ V[/tex]
We need to calculate the speed of electron
Using energy conservation
[tex]U=eV=\dfrac{1}{2}mv^2[/tex]
Put the value into the formula
[tex]1.6\times10^{-19}\times30.06=\dfrac{1}{2}\times9.1\times10^{-31}\times v^2[/tex]
[tex]v^2=\dfrac{1.6\times10^{-19}\times30.06\times2}{9.1\times10^{-31}}[/tex]
[tex]v=\sqrt{1.057\times10^{13}}[/tex]
[tex]v=3.2\times10^{6}\ m/s[/tex]
Hence, The speed of electron is [tex]3.2\times10^{6}\ m/s[/tex]
