Ncert Exercises & Solutions

Question 6.12:

An electron and a proton are detected in a cosmic ray experiment, the first with kinetic energy 10 keV, and the second with 100 keV. Which is faster, the electron or the proton? Obtain the ratio of their speeds. (electron mass = $9.11 \times 10^{- 31} k g$ , proton mass = $1.67 \times 10^{- 27} k g$ , 1 eV = $1.60 \times 10^{- 19} J$ ).

G i v e n, K_{e} = 10 k e V, K_{p} = 100 k e V m_{e} = 9.11 \times 10^{- 31} k g, m_{p} = 1.67 \times 10^{- 27} k g N o w, K = \frac{1}{2} m v^{2} \Rightarrow v = \sqrt{\frac{2 K}{m}} \Rightarrow \frac{v_{e}}{v_{p}} = \sqrt{\frac{K_{e}}{K_{p}} \times \frac{m_{p}}{m_{e}}} = \sqrt{\frac{10 \times 1.67 \times 10^{- 27}}{100 \times 9.11 \times 10^{- 31}}} \Rightarrow \frac{v_{e}}{v_{p}} = 13.54 o r, v_{e} = 13.54 v_{p}

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