Question

What is the average particle energy needed to observe unification of forces, estimated to be 10¹⁹ GeV? To do this, calculate the rest mass in kilograms of a particle that has a rest mass of 10¹⁹GeV/c²

(a)1.79×10−⁸kg
(b)2.25×10−⁸kg
(c)3×10−⁸kg
(d)3.57×10−⁸kg

Answer 1

To find the rest mass in kilograms of a particle with a rest mass of 10¹⁹ GeV/c², use the equation E=mc² and convert the units. The rest mass is approximately 1.99x10² palanquin ¹⁹⁻⁸ kg. This mass is approximately 1.19x10¹² times the mass of a hydrogen atom.

Step-by-step explanation:

To calculate the rest mass in kilograms of a particle with a rest mass of 10¹⁹ GeV/c², we can use the equation E=mc², where E is the energy, m is the mass, and c is the speed of light. Rearranging the equation, we have m = E/c². Plugging in the given values, we have m = (10¹⁹ GeV)/(3x10⁸ m/s)².

Simplifying this, we get m = 10¹⁹ GeV / 9x10¹⁶ m²/s². To convert this to kilograms, we can use the conversion factor 1 GeV/c² = 1.783x10⁻²⁷ kg. Multiplying the mass in GeV by the conversion factor, we get m = (10¹⁹ GeV / 9x10¹⁶ m²/s²) x (1.783x10⁻²⁷ kg/1 GeV/c²).

Evaluating this expression, we get m = 1.99x10² palanquin ¹⁹⁻⁸ kg. Therefore, the rest mass of the particle is approximately 1.99x10² palanquin ¹⁹⁻⁸ kg.

To find how many times the mass of a hydrogen atom this is, we can divide the rest mass of the particle by the rest mass of a hydrogen atom.

The rest mass of a hydrogen atom is approximately 1.673x10⁻²⁷ kg. Dividing the mass of the particle by the mass of a hydrogen atom, we have (1.99x10² palanquin ¹⁹⁻⁸ kg)/(1.673x10⁻²⁷ kg).

Evaluating this expression, we get a value of approximately 1.19x10¹². Therefore, the rest mass of the particle is approximately 1.19x10¹² times the mass of a hydrogen atom.