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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 1970s 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.)
Answer:

Wavelength of a proton or a neutron, image461 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

Rest mass energy of an electron:

image462 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

image463 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2 Planck’s constant, h= 6.6 × 10 – 34Js

image464 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

Speed of light, c= image465 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

The momentum of a proton or a neutron is given as:

image466 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

image467 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

The relativistic relation for energy (E) is given as:

image468 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

image469 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

image470 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

image471 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

image472 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

image473 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

image474 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

Thus, the electron energy emitted from the accelerator at Stanford, USA might be of the order of 1.24 BeV.

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