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The wavelength of a probe is roughly a measure of the size of a structure that it can probe in some detail. The quark structure of protons and neutrons appears at the minute length-scale of 10^(-15)m or less. This structure was first probed in early 1970’s using high energy electron beams produced by a linear accelerator at Stanford, USA. Guess what might have been the order of energy of these electron beams. (Rest mass energy of electron = 0.511 MeV.) |
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Answer» <P> Solution :Here `lambda=10^(-15)m,h=6.63xx10^(-34)`Js`c=3xx10^(8)ms^(-1)` `implies` Momentum, `p=(h)/(lambda)=(6.63xx10^(-34))/(10^(-15))` `therefore p=6.63xx10^(-19)kg ms^(-1)` `implies` Rest mass energy of electron, `m_(0)c^(2)=0.511 MeV` `therefore m_(0)c^(2)=0.511xx10^(6)xx1.6xx10^(-19)J` `=-0.8176xx10^(-13)J` `implies` Energy of electron according to EQUATION relativity, `E=sqrt(p^(2)c^(2)+m_(0)^(3)c^(4))` `therefore E^(2)=p^(2)c^(2)+m_(0)^(2)c^(4)=p^(2)c^(2)+(m_(0)c^(2))^(2)` `=(6.63xx10^(-19))^(2)xx(3xx10^(8))^(2)` `+(0.8176xx10^(-13))^(2)` `=395.9xx10^(-28)=0.66846xx10^(-26)` Neglecting rest mass energy, `E^(2)=395.6xx10^(-22)` `therefore E=19.8896xx10^(-11)` `therefore E~~19.89xx10^(-11)J` `therefore E=(19.89xx10^(-11))/(1.6xx10^(-10))BEV` `[because 1 BeV=1.6xx10^(-10)]` Thus energy obtained from accelerator should be of the order of BeV. |
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