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

Using the formula,

Momentum of the particle is,

p = \frac{h}{λ} = \frac{6.63 \times 10^{- 34} Js}{10^{- 15} m}

= 6.63 \times 10^{- 19} Kg {ms}^{- 1}

Now, the relativistic formula for energy gives us:

E^{2} = c^{2} p^{2} + m_{0}^{2} c^{4}

\Rightarrow E^{2} = 9 \times (6.63)^{2} \times 10^{- 22} + (0.511 \times 1.6)^{2} \times 10^{- 26}

≃ 9 \times (6.63)^{2} \times 10^{- 22}

the second term (rest mass energy) being negligible.

Therefore,

E = 1.989 \times 10^{- 10} J

E = \frac{1.989 \times 10^{- 10}}{1.6 \times 10^{- 11}} BeV = 1.24 BeV .

Thus, the order of energy of these electron beams is of the order of few Bev.

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