Question

The average energy of helium is E= 2.89×TEN TO THE POWER 21 JOULE.Calculate their average speed v.

Answer 1

Answer on Question #73215 - Physics / Molecular Physics

The average energy of helium is $\bar{E} = 2.89 \times 10^{-21} \, \mathrm{J}$. Calculate their average speed $v$.

Solution:

The average energy

$$\bar{E} = \frac{m \bar{v}^2}{2}$$

The average speed

$$\bar{v} = \sqrt{\frac{2 \bar{E}}{m}}$$

The mass of helium atom is

$$m = \frac{\mu}{N_A} = \frac{0.004}{6.02 \times 10^{23}} = 6.64 \times 10^{-27} \, \mathrm{kg}$$

Finally

$$\bar{v} = \sqrt{\frac{2 \times 2.89 \times 10^{-21}}{6.64 \times 10^{-27}}} = 933 \, \mathrm{m/s}$$

Answer: $\bar{v} = 933 \, \mathrm{m/s}$.

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