Adeuteron, 21h, is the nucleus of a hydrogen isotope and consists of one proton and one neutron. the plasma of deuterons in a nuclear fusion reactor must be heated to about 3.02×108 k . what is the rms speed of the deuterons? express your answer using two significant figures.

The thermal energy and the conservation of energy allows to find the average speed of the deuteron atoms is:

            v = 1.9 10⁶ m / s

The thermal energy of a particle is given by the Boltzmann energy partition relation, which in three dimensions is:

           E =  kT

Energy kinetic s the energy of movement and its expression is:

           K = ½ m v²

They indicate that the temperature of the plasma is T = 3.02 10⁸ K.

If there are no losses, the energy is conserved.

          K = E

          ½ m v² =  kT

          v =  

The mass of deuteron is m = 2.013 u

Let's reduce to kg

            m = 2.013 u (  )

            m = 3.5358 10⁻²⁷ kg

We take the mass of a deuterium to 1 mole, multiplying by Avogador's number.

             m = 3.5358 10⁻²⁷  6.022 10²³

             m = 2.129 10⁻³ kg / mol

We calculate

             v =  

             v =

             v = 1.88 10⁶ m / s

They ask for the result with two significant figures.

             v = 1.9 10⁶ m / s

In conclusion using thermal energy and conservation of energy we can find the average speed of deuteron atoms is:

            v = 1.9 10⁶ m / s

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Explanation:

Data:

T = 3.02 × 10⁸ K

M = 2.013 × 10⁻³ kg/mol

Calculation: