In an experimental inertial-confinement fusion reactor,inertial confinement has a useful duration of $\tau$ = 2.0 $\times$ 10^-10 s.What must the density of the fusible material be in order to meet Lawson's criterion? A)2.0 $\times$ 10²⁴ particles/cm³ B)5.0 $\times$ 10²³ particles/cm³ C)6.0 $\times$ 10²³ particles/cm³ D)2.5 $\times$ 10²³ particles/cm³ E)7.0 $\times$ 10²³ particles/cm³

Question

Quizplus · Accepted Answer

Lawson's criterion states that the product of the density and the confinement time must be greater than a certain value to achieve fusion. Mathematically, it can be expressed as nτ > (T/2)exp(Ea/kT).

In this problem, the confinement time (τ) is given as 2.0 x 10^-10 s. We need to find the density (n) required to meet Lawson's criterion.

We are not given the temperature (T) and activation energy (Ea), so we cannot solve for the product on the right-hand side of the inequality. However, we can use the given answer choices to estimate the required density.

Answer choice B gives a value of 5.0 x 10^23 particles/cm^3 s, which is in the same order of magnitude as typical densities required for fusion. Therefore, B is the best choice.

Note that the other answer choices either give densities that are too low (A, D) or too high (C, E) to be realistic for fusion.

In an Experimental Inertial-Confinement Fusion Reactor,inertial Confinement Has a Useful τ\tauτ

In an Experimental Inertial-Confinement Fusion Reactor,inertial Confinement Has a Useful $\tau$