Class 12 Physics
CBSE and UP Board
Dual Nature of Radiation and Matter
Chapter-11 Exercise 11.34
NCERT Solutions for Class 12 Physics Chapter 11 Question-34
Additional Exercise
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.)
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Wavelength of a proton or a neutron, λ ≈ 10-15 m
Rest mass energy of an electron:
moc2 = 0.511 MeV = 0.511 x 106x 1.6 x 10⁻19 = 0.8176 x 10⁻13 J
Planck’s constant, h = 6.6 x 10⁻34Js
Speed of light, c = 3x 10s m/s
The momentum of a proton or a neutron is given as:
p=h/λ = (6.6 x 10⁻34)/ 10-15
= 6.6 x 10⁻19 kg m/s
The relativistic relation for energy (E) is given as:
E = p²c² + m²oc⁴
= (6.6 x 10⁻19 x 3 x 10⁸ )²+ (0.8176 x 10⁻13)² = 392.04 x 10⁻²² + 0.6685 x 10⁻²6
≈392.04 x 10⁻²²
Therefore ,E = 1.98 x 10⁻¹⁰
= ( 1.98 x 10⁻¹⁰ )/(1.6 x 10⁻19) = 1.24 x 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.