What is the average kinetic energy (in J) of helium atoms in a region of the solar corona where the temperature is 6.30 ✕ 105 K?

The average kinetic energy (\(KE\)) of particles in a gas can be found using the formula:

\[
KE = \frac{3}{2} k_B T
\]

where:
- \(k_B\) is the Boltzmann constant (\(1.38 \times 10^{-23} \, \text{J/K}\)),
- \(T\) is the temperature in kelvin (K).

Given:
\[
T = 6.30 \times 10^5 \, \text{K}
\]

### Calculation
1. Substitute the values into the formula:

   \[
   KE = \frac{3}{2} \times (1.38 \times 10^{-23}) \times (6.30 \times 10^5)
   \]

2. Calculate each step:
   - \(1.38 \times 10^{-23} \times 6.30 \times 10^5 = 8.694 \times 10^{-18}\)
   - Multiply by \(\frac{3}{2}\):

     \[
     KE = \frac{3}{2} \times 8.694 \times 10^{-18} = 1.3041 \times 10^{-17} \, \text{J}
     \]

### Answer
The average kinetic energy of helium atoms in the given region of the solar corona is approximately:

\[
KE \approx 1.30 \times 10^{-17} \, \text{J}
\]

Would you like further details or have any questions?

Here are some related questions to expand your understanding:
1. How does the average kinetic energy of particles change with temperature?
2. What is the significance of the Boltzmann constant in thermal physics?
3. How would the kinetic energy differ for a different type of atom or molecule at the same temperature?
4. How does temperature affect the speed of helium atoms in the solar corona?
5. How is this concept applied in understanding thermal motions in gases?

**Tip:** Remember, the kinetic energy of particles in a gas is directly proportional to temperature—higher temperatures result in higher kinetic energy.

What is the average kinetic energy (in J) of helium atoms in a region of the solar corona where the temperature is 6.30 ✕ 10^5 K?

Calculate the average kinetic energy of helium atoms in the solar corona with a temperature of 6.30 ✕ 10^5 K using the kinetic energy formula KE = (3/2) * k_B * T. This detailed solution is suitable for high school students learning thermodynamics and gas laws.

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