Question

Nuclear fusion, the energy source of the Sun, hydrogen bombs, and fusion reactors, occurs much more readily when the average kinetic energy of the atoms is high—that is, at high temperatures. Suppose you want the atoms in your fusion experiment to have average kinetic energies of 5 X 10²¹ , J . What temperature is needed?

a) 3000 , K
b) 5000 , K
c) 8000 , K
d) 12000 , K

Answer 1

The temperature needed for atoms to have an average kinetic energy of 6.40 × 10^-14 J in a fusion experiment is approximately 6164 K, thus the closest given option is (c) 8000 K.

Step-by-step explanation:

To determine the temperature needed for atoms in a fusion experiment to have average kinetic energies of 6.40 × 10-14 J, we use the fact that the average kinetic energy (KE) of particles is related to the absolute temperature (T) by the equation KE = (3/2) kT, where k is the Boltzmann constant (1.38 × 10-23 J/K). To solve for T, we rearrange the equation to T = (2/3) (KE/k) and substitute in the given kinetic energy value:

T = (2/3) (6.40 × 10-14 J) / (1.38 × 10-23 J/K)
Calculating this gives us a temperature of approximately 6164 K, which means the correct option is (c) 8000 K since it is the closest to our calculated value and the options provided are discretized rather than continuous values.