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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 $10^{-15} \mathrm{~m}$ or less. This structure was first probed in the 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 = $0.511 \mathrm{MeV}$ ).
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 $10^{-15} \mathrm{~m}$ or less. This structure was first probed in the 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 = $0.511 \mathrm{MeV}$ ).
CBSE | Class 12 | Dual Nature of Radiation and Matter | NCERT | Physics
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 $10^{-15} \mathrm{~m}$ or less. This structure was first probed in the 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 = $0.511 \mathrm{MeV}$ ).

Wavelength of the proton or neutron is given as $\lambda \approx 10^{-15} \mathrm{~m}$

Rest mass-energy of an electron will be calculated as:

${{m}_{o}}{{c}^{2}}=0.511MeV$

$=0.511\times {{10}^{6}}\times 1.6\times {{10}^{-19}}$

$=0.8176\times {{10}^{-13}}J$


Planck’s constant, $\left.h=6.6 \times 10^{-34}\right\rfloor \mathrm{s}$
Speed of light, $c=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$
The momentum of the proton or a neutron is given by the expression,

$p=h/\lambda $

\[=6.6\times {{10}^{-34}}/{{10}^{-15}}\] $=6.6\times {{10}^{-19}}kgm/s$


The expression for the relativistic relation for energy (E) is given as

${{E}^{2}}={{p}^{2}}{{c}^{2}}+{{m}_{0}}^{2}{{C}^{4}}$

$={{(6.6\times {{10}^{-19}}\times 3\times {{10}^{8}})}^{2}}+{{(0.8176\times {{10}^{-13}})}^{2}}$

$=392.04\times {{10}^{-22}}+0.6685\times {{10}^{-26}}$

$\approx 392.04\times {{10}^{-22}}$

$E=19.8\times {{10}^{-11}}$

$=19.8\times {{10}^{-11}}/1.6\times {{10}^{-19}}$

$=12.375\times {{10}^{8}}eV$


Order of energy of these electron beams is $12.375 \times 10^{8} \mathrm{eV}$

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