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NCERT Class XII Chapter
Dual Nature of Radiation and Matter
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Question : 34 of 37
Marks: +1, -0
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 10−1510^{-15} m or less. This structure was first probed in early 1970’s using high energy electron beam produced by a linear accelerator at Standford, USA. Guess what might have been the order of energy of these electron beams. (Rest mass energy of electron = 0.511 MeV).
Solution:  
∴ Momentum of electron associated with given wavelength
p = hλ\frac{h}{\lambda} = .63×10−34Js10−15m\frac{.63 \times 10^{-34} \mathrm{Js}}{10^{-15} \mathrm{m}} = .63 × 10−19 kg m s−110^{-19} \,\mathrm{kg\,m\,s^{-1}}
Rest mass energy of electron,
m0c2m_0 c^2 = 0.511 MeV = 0.511 × 10610^6 × 1.6 × 10−1910^{-19} J = 0.511 × 1.6 × 10−1310^{-13} J.
We use the relativistic formula for the energy of electron, i.e.,
E = c2p2+m02c4\sqrt{c^2 p^2 + m_0^2 c^4}
E =
9×(6.63)2×10−22+(0.511×1.6)2×10−26\sqrt{9 \times (6.63)^2 \times 10^{-22} + (0.511 \times 1.6)^2 \times 10^{-26}}
Second term showing rest mass energy is negligible.
Energy, E = 1.989 × 10−1010^{-10} J = 1.24 BeV
Thus, energies acquired by electron from the given accelerator must have been of the order of a few BeV.
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