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Work, Energy And Power

Question
CBSEENPH11017201

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).

Solution

Given that,
Kinetic energy, straight K subscript straight e equals 10 KeV space equals space 10 cross times 1.6 cross times 10 to the power of negative 16 end exponent straight J 
                          equals 1.6 cross times 10 to the power of negative 15 end exponent straight J 
K.E of proton, straight K subscript straight p space equals space 100 KeV space equals space 100 cross times 1.6 cross times 10 to the power of negative 16 end exponent straight J 
                        space space equals 1.6 cross times 10 to the power of negative 14 end exponent straight J 
K.E is given by, 
             space space space straight K equals 1 half mv squared 
rightwards double arrow            straight v equals square root of fraction numerator 2 straight K over denominator straight m end fraction end root 
∴ ratio of their speed is given by,
                   space space space straight v subscript straight e over straight v subscript straight p equals square root of straight K subscript straight e over straight K subscript straight p straight m subscript straight p over straight m subscript straight e end root equals square root of 1 over 10 cross times fraction numerator 1.67 cross times 10 to the power of negative 27 end exponent over denominator 9.1 cross times 10 to the power of negative 31 end exponent end fraction end root 
        = 13.54 
Thus electron is faster than proton by a magnitude of 13.54.