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Physics345
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Homework Statement
In a TV tube, an electric potential difference accelerates electrons from a rest position towards a screen. Just before striking the screen, the electrons have a wavelength of 10×〖10〗^(-11) m. Find the electric potential difference.
Homework Equations
∆E_K=q∆V
λ=h/mv
The Attempt at a Solution
given: e=1.6×10^(-19) Js λ=1.0×10^(-11) m m=9.11×10^(-31) kg h=6.63×10^(-34) Js
λ=h/mv
v=h/λm
v=(6.63×10^(-34) Js )/((1.0×10^(-11) m)(9.11×10^(-31) kg))
v=7.3×10^7 m⁄s
∆E_K=q∆V
E_K2-E_K1=e∆V Rest position so E_K1=0
∆V=(1/2 mv^2)/e
∆V=(1/2 (9.11×10^(-31) kg) (7.3×10^7 m⁄s)^2)/(1.6×10^(-19) Js)
∆V=1.52×10^4 V Therefore the electric potential difference is 1.52×10^4 V