An electron and a proton are detected in a cosmic ray experiment, the first with kinetic energy $10 k e V$ , and the second with $100 k e V$ . The ratio of their speeds is
(where $m_{e}$ and $m_{p}$ are masses of electrons and proton respectively).

\sqrt{\frac{1}{10} \frac{m_{e}}{m_{p}}}

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\sqrt{\frac{1}{10} \frac{m_{p}}{m_{e}}}

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\frac{1}{10} \frac{m_{e}}{m_{p}}

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\frac{1}{10} \frac{m_{p}}{m_{e}}

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Solution

The correct option is B $\sqrt{\frac{1}{10} \frac{m_{p}}{m_{e}}}$
$V = \sqrt{\frac{2 M}{K_{E}}}$
$M =$ Mass
$K_{E} =$ Kinetic energy
$V =$ Speed of object
$\frac{V_{1}}{V_{2}} = \sqrt{\frac{2 M_{e}}{K_{e}} \times \frac{K_{e}}{2 M_{P}}} = \sqrt{\frac{100 \times M_{e}}{10 \times M_{P}}} = \frac{V_{1}}{V_{2}} \frac{V_{1}}{V_{2}} = \sqrt{\frac{1}{10} \times \frac{M_{e}}{M_{P}}} \frac{V_{2}}{V_{1}} = \sqrt{\frac{1 M_{P}}{10 M_{e}}}$

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Similar questions

Q. An electron and a proton are detected in a cosmic ray experiment, the first with kinetic energy

10 k e V

, and the second with

100 k e V

. Which is faster the electron or the proton? Obtain the ratio of their speeds. (

m_{e} = 9.1 \times 10^{- 31} k g, m_{p} = 1.67 \times 10^{- 27} k g, 1 e V = 1.6 \times 10^{- 19} J

)

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 × 10^–31 kg, proton mass = 1.67 × 10^–27 kg, 1 eV = 1.60 × 10^–19 J).