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 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.)

Answer 1

here, wavelength, λ = 10^-15 m

from De-broglie's wavelength, λ = h/p

where h is Plank's constant.i.e., h = 6.63 × 10^-34 J.s

and p is momentum of electron associated with wavelength λ

so, p = h/λ

= (6.63 × 10^-34)/(10^-15)

= 6.63 × 10^-19 Kgm/s

rest mass energy of electron, ∆mc² = 0.511 MeV = 0.511 × 10^6 × 1.6 × 10^-19J

= 0.511 × 1.6 × 10^-13 J

now use the relativistic formula for the energy of electron.i.e., E = $\sqrt{c^2p^2+(\Delta mc^2)^2}$

= √{(3 × 10^8)² × (6.63 × 10^-19)² + (0.511 × 1.6 × 10^-13)²}

= 1.989 × 10^-10J

we know, 1 eV = 1.6 × 10^-19J

so, E = 1.989 × 10^-10/(1.6 × 10^-19)

= 1.24 BeV

it is clear that energy acquired by electron from the given accelerator must have been of the order of a few BeV.

Answer 2

Answer:

ur ans is in the attachment

Explanation:

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