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Question

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).

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Solution

Given:

The kinetic energy of the electron, Ke =10 keV, the kinetic energy of the proton, K p =100 keV, the mass of the electron, m e =9.11× 10 −31  kg and the mass of the proton, m p =1.67× 10 −27  kg.

The kinetic energy of the electron can be given as, Ke=12mev2e,ve=2Keme ...(1)

The kinetic energy of the proton can be given as, Kp=12mpv2p,vp=2Kpmp ...(2)

By dividing equation (1) by equation (2), we get

vevp=2Kemp2Kpme

By substituting the given values in the above equation, we get

vevp=2(10)×1.67×10272(100)×9.11×1031

ve=13.5vp

The above relation shows that the electron is moving faster than the proton.


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