An electron is accelerated to a speed of 4.23 × 10^6 ms –1 from rest by a potential difference. Calculate the potential difference
e=1.6∗10−19Ce = 1.6*10^{-19}Ce=1.6∗10−19C
v=4.23∗106msv = 4.23*10^6 \frac{m}{s}v=4.23∗106sm
m=9.1∗10−31kgm = 9.1*10^{-31}kgm=9.1∗10−31kg
Δϕ=\Delta \phi =Δϕ= ?
A=ΔEA=\Delta EA=ΔE
eΔϕ=mv22→Δϕ=mv22e=9.1∗10−31∗(4.23)2∗10122∗1.6∗10−19=51Ve\Delta \phi = \large\frac{mv^2}{2} \to \Delta \phi = \large\frac{mv^2}{2e}=\frac{9.1*10^{-31}*(4.23)^2*10^{12}}{2*1.6*10^{-19}}=51VeΔϕ=2mv2→Δϕ=2emv2=2∗1.6∗10−199.1∗10−31∗(4.23)2∗1012=51V
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