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 6.40×10−¹⁴ J. What temperature is needed?

a) 1000 K
b) 2000 K
c) 3000 K
d) 4000 K

Answer 1

The temperature needed for atoms to have an average kinetic energy of 6.40 × 10⁻¹⁴ J is approximately 3.70 × 10⁹ K.

Step-by-step explanation:

In nuclear fusion, the average kinetic energy of the atoms needs to be high, which is achieved at high temperatures.

To find the necessary temperature, we can use the formula:

Kinetic energy per atom = (3/2) × k × T

where k is the Boltzmann constant (1.38 × 10⁻²³ J/K) and T is the temperature in kelvin (K).

Using the given average kinetic energy of 6.40 × 10⁻¹⁴ J, we can rearrange the formula to solve for T:

T = (2 × average kinetic energy per atom) / (3 × k) = (2 × 6.40 × 10⁻¹⁴ J) / (3 × 1.38 × 10⁻²³ J/K) = 3.70 × 10⁹ K

The temperature needed for the atoms to have an average kinetic energy of 6.40 × 10⁻¹⁴ J is approximately 3.70 × 10⁹ K.