Question

Integrated Concepts Fusion probability is greatly enhanced when appropriate nuclei are brought close together, but mutual Coulomb repulsion must be overcome. This can be done using the kinetic energy of high-temperature gas ions or by accelerating the nuclei toward one another.

(a) Calculate the potential energy of two singly charged nuclei separated by 1.00×10–12 m by finding the voltage of one at that distance and multiplying by the charge of the other.
(b) At what temperature will atoms of a gas have an average kinetic energy equal to this needed electrical potential energy?

Answer 1

(a) 2.3 x 10^-16 J

(b) 1.1 x 10^7 K

Step-by-step explanation:

charge, q = 1.6 x 10^-19 C

distance, r = 10^-12 m

(a) Let the potential energy is U.

`U = (k q q)/(r^2)\\\\U = (9* 10^(9)* 1.6* 1.6* 10^(-38))/(10^(-12))\\\\U = 2.3* 10^(-16) J`

(b) Let the temperature is T.

`U = K = (3)/(2) kT\\\\2.3 * 10^(-16) = 1.5* 1.38* 10^(-23) T\\\\T = 1.1* 10^7 K`