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Question
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.)
Solution
Wavelength of a proton or a neutron, λ ≈ 10−15 m
Rest mass energy of an electron:
m0c2 = 0.511 MeV
= 0.511 × 106 × 1.6 × 10−19
= 0.8176 × 10−13 J
Planck’s constant, h = 6.6 × 10−34 Js
Speed of light, c = 3 × 108 m/s
The momentum of a proton or a neutron is given as:
`"p" = "h"/lambda`
= `(6.6 xx 10^(-34))/10^(-15)`
= 6.6 × 10−19 kg m/s
The relativistic relation for energy (E) is given as:
`"E"^2 = "p"^2"c"^2 + "m"_0^2"c"^4`
= `(6.6 xx 10^(-19) xx 3 xx 10^8)^2 + (0.8176 xx 10^(-13))^2 `
= `392.04 xx 10^(-22) + 0.6685 xx 10^(-26)`
≈ 392.04 × 10−22
∴ E = 1.98 × 10−10 J
= `(1.98 xx 10^(-10))/(1.6 xx 10^(-19))`
= 1.24 × 109 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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