Question

A proton and electron have kinetic energy equal to 10⁵eV and 10⁴eVrespectively which of them moves faster? also calculate the ration of their speeds. Given mass of electron 9.11 *10^-31 mass of proton 1.67*10^{-27 kg} And 1.6* 10^-19 J

Answer 1

$$\begin{gathered} \frac{K{E}_{proton}}{K{E}_{electron}}=\frac{{10}^5}{{10}^4}=10 \\ \frac{{\displaystyle \frac{1}{2}}\times 1.67\times \times {10}^{-27}\times {v_p}^2}{\frac{1}{2}\times 9.11\times \times {10}^{-31}\times {v_e}^2}=10 \\ \frac{{\mathbf{v}}_{\mathbf{p}}}{{\mathbf{v}}_{\mathbf{e}}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{0}\mathbf{.}\mathbf{074} \\ or, \\ \frac{{\mathbf{v}}_{\mathbf{e}}}{{\mathbf{v}}_{\mathbf{p}}\mathbf{}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{13}\mathbf{.}\mathbf{51} \\ or, \\ {v}_e=13.51v_p \\ Thus, \\ thevelocityofanelectronismorethanthevelocityoftheproton. \end{gathered}$$