Chemistry, 22.06.2019 12:20 jessicasbss6840

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.

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Answer from: brendacauani12345

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 = $\frac{3}{2}$ 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 = $\frac{3}{2}$ kT

v = $\sqrt{\frac{3 kT}{m} }$

$\frac{1.66 \ 10^{-27} kg}{1 u}$

The mass of deuteron is m = 2.013 u

Let's reduce to kg

m = 2.013 u ( $\frac{1.66 \ 10^{-27} kg}{1 uy}$ )

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 = $\sqrt{ \frac{3 \ 8.314 \ 3.02 \ 10^8 }{2.129 \ 10^{-3} } }$

v = $\sqrt{3.538 \ 10^{12}}$

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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Answer from: tommyaberman

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

Explanation:

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

Data:

T = 3.02 × 10⁸ K

M = 2.013 × 10⁻³ kg/mol

Calculation:

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

Answer from: Quest

first let us lay out the formula for potential

and kinetic energy:

pe = mgh

ke = (mv^2)/2

where: m=mass, v=velocity, g=gravitational

acceleration, h=height

calculating for mass using the known values of

pe:

340j = m (9.81 m/s^2) (50ft) (1m/3.28ft)

m = 2.27 kg

the law of conservation of energy states that

energy is neither created nor destroyed. therefore, the change in kinetic

energy from 50 ft to 35 ft would be equal to the change in potential energy

from 50 ft to 35 ft. however it would be opposite in signs since one is losing

while other is gaining.

ke(35ft) – ke(50ft) = - [ pe(35ft) – pe(50ft]

ke(50ft) = 0 since the brick is initially at rest

ke(35ft) = 340j - 2.27kg (9.81 m/s^2) (35ft)

(1m/3.28 ft)

ke(35ft)

= 102.38 j

Answer from: Quest

They can measure the amount of energy gained or lost

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Adeuteron, 21h, is the nucleus of a hydrogen isotope and consists of one proton and one neutron. the...

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