Answer:
[tex]1.9 \times 10^{6}\text{ m/s}[/tex]
Explanation:
[tex]v_{\text{rms}} = \sqrt{\dfrac{3RT}{M}[/tex]
Data:
T = 3.02 × 10⁸ K
M = 2.013 × 10⁻³ kg/mol
Calculation:
[tex]v_{\text{rms}} = \sqrt{\dfrac{3\times 8.314\text{ J}\cdot\text{K}^{-1} \text{mol}^{-1} \times 3.02 \times 10^{8} \text{ K}}{2.014 \times 10^{-3} \text{ kg}\cdot \text{mol}^{-1}}}\\\\\\=\sqrt{3.740\times 10^{12} \text{ (m/s)}^{2}} = 1.9 \times 10^{6}\text{ m/s}[/tex]
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 = [tex]\frac{3}{2}[/tex] 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 = [tex]\frac{3}{2}[/tex] kT
v = [tex]\sqrt{\frac{3 kT}{m} }[/tex]
[tex]\frac{1.66 \ 10^{-27} kg}{1 u}[/tex]
The mass of deuteron is m = 2.013 u
Let's reduce to kg
m = 2.013 u ( [tex]\frac{1.66 \ 10^{-27} kg}{1 uy}[/tex])
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 = [tex]\sqrt{ \frac{3 \ 8.314 \ 3.02 \ 10^8 }{2.129 \ 10^{-3} } }[/tex]
v = [tex]\sqrt{3.538 \ 10^{12}}[/tex]
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
Learn more here: brainly.com/question/18989562
