Use the following values for mass and charge: an electron has mass m e = 9.11×10

Question

Use the following values for mass and charge: an electron has mass me = 9.11×10-31 kg and charge -e, a proton has mass mp = 1.67×10-27 kg and charge +e, an alpha particle has mass malpha = 6.65×10-27 kg and charge +2e, where e = 1.60×10-19 C. An electron is released from rest in a vacuum between two flat, parallel metal plates that are 16.0 cm apart and are maintained at a constant electric potential difference of 810 Volts.

If the electron is released at the negative plate, what is its speed just before it strikes the positive plate?

What is the kinetic energy of the electron in units of eV?

Explanation / Answer

(a) The potential of the electron at release = kinetic at the upper plate

so V*q = 1/2*m*v^2

so v = sqrt(2*V*q/m) = sqrt(2*810*1.60x10^-19/9.11x10^-31) = 1.69x10^7m/s

(b) From the definition of an electron volt we E = 810 eV

[or you can convert from Joules to eV

K = 1/2*m*v^2 = 1/2*9.11x10^-31*(1.69x10^7)^2 = 1.296x10^-16J

so in eV,

E = 1.296x10^-16/1.60x10^-19 = 810 eV]

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