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.)

Explanation

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)]` `therefore E=~~1.24 BeV`
Thus energy obtained from accelerator should be of the order of BeV.