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The wavelength of a probe is roughly a ...

The wavelength of a probe is roughly a measure of the size of structure that it can probe in some detail. The quarks structure of photons 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 beam produced by a linear accelerator at Stanford's USA. Guess what might have been the order of energy of these electron beams (Rest mass energy of electron=0.511 eV).

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Wavelength of a proton or a neutron , `lambda~~10^(-15)m`
Rest mass energy of an electron :
`m_0c^2=0.511 MeV`
`=0.511xx10^6xx1.6xx10^(-19)`
`=0.8176xx10^(-13)J`
Planck's constant, h=`6.6xx10^(-34) Js`
Speed of light, `c=3xx10^8` m/s
The momentum of a proton or a neutron is given as : `p=h/lambda`
`=(6.6xx10^(-34))/10^(-15)=6.6xx10^(-19)` kg m/s
The relativistic relation for energy (E) is given as :
`E^2=p^2c^2+m_0^2c^4`
`=(6.6xx10^(-19)xx3xx10^8)+(0.8176xx10^(-13))^2`
`=392.04xx10^(-22) +0.6685 xx 10^(-26)`
`~~392.04xx10^(-22)`
`therefore E=1.98xx10^(-10) J`
`=(1.98xx10^(-10))/(1.6xx10^(-19))`
`=1.24xx10^9` eV = 1.24 BeV
Thus, the electron energy emitted from the accelerator at Stanford , USA might be of the order of 1.24 BeV.
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