   Chapter 34, Problem 26PE

Chapter
Section
Textbook Problem

The characteristic length of entities in Superstring theory is approximately (a) Find the energy in GeV of a photon of this wavelength.(b) Compare this with the average particle energy of 1019 GeV needed for uni?cation of forces.

To determine

(a)

The energy of the photon in GeV.

Explanation

Given:

Speed of light, c=3×108m/s

Plank's constant, h=6.62×1034J-s

Wavelength of the photon, λ=1035m

Formula used:

Formula to calculate the energy of the photon,

E=hcλ ...... (I)

Where,

• h is Plank's constant.
• λ is wavelength of the photon.
• c is speed of light.

Calculation:

Unified force energy evaluated at high energy and having wavelength on the order of 1035m . So, superstrings should have the wavelength smaller than or equal to 1035m.

Substitute 6.62×1034J-s for h , 3×108m/s for c , and 1035m for λ in equation (I)

To determine

(b)

The comparison of the energy of the photon with average particle energy needed for unification of forces.

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