Question

A deuteron, 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.

Answer 1

Answer:

$1.9 \times 10^{6}\text{ m/s}$

Explanation:

$v_{\text{rms}} = \sqrt{\dfrac{3RT}{M}$

Data:

T = 3.02 × 10⁸ K

M = 2.013 × 10⁻³ kg/mol

Calculation:

$v_{\text{rms}} = \sqrt{\dfrac{3\times 8.314\text{ J}\cdot\text{K}^{-1} \text{mol}^{-1} \times 3.02 \times 10^{8} \text{ K}}{2.014 \times 10^{-3} \text{ kg}\cdot \text{mol}^{-1}}}\\\\\\=\sqrt{3.740\times 10^{12} \text{ (m/s)}^{2}} = 1.9 \times 10^{6}\text{ m/s}$