The rms speed of helium on the surface of the sun is `6.01 km//s`. Make an estimate of the surface temperature of the sun.

Explanation

To estimate the surface temperature of the Sun using the given RMS speed of helium, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- RMS speed of helium, \( V_{\text{rms}} = 6.01 \, \text{km/s} \)
- Convert this speed to meters per second:
\[ V_{\text{rms}} = 6.01 \times 10^3 \, \text{m/s} \]

2. **Recall the Formula for RMS Speed:**
The formula for the root mean square speed is given by:
\[ V_{\text{rms}} = \sqrt{\frac{3RT}{M}} \]
where:
- \( R \) is the gas constant (8.31 J/(mol·K)),
- \( T \) is the temperature in Kelvin,
- \( M \) is the molar mass of helium.

3. **Determine the Molar Mass of Helium:**
The molar mass of helium is:
\[ M = 4 \times 10^{-3} \, \text{kg/mol} \]

4. **Square Both Sides of the RMS Speed Equation:**
To eliminate the square root, square both sides:
\[ V_{\text{rms}}^2 = \frac{3RT}{M} \]

5. **Rearrange the Equation to Solve for Temperature \( T \):**
Rearranging gives:
\[ T = \frac{V_{\text{rms}}^2 \cdot M}{3R} \]

6. **Substitute the Known Values:**
Substitute \( V_{\text{rms}} \), \( M \), and \( R \) into the equation:
\[ T = \frac{(6.01 \times 10^3)^2 \cdot (4 \times 10^{-3})}{3 \cdot 8.31} \]

7. **Calculate \( V_{\text{rms}}^2 \):**
\[ (6.01 \times 10^3)^2 = 36.1201 \times 10^6 = 3.61201 \times 10^7 \, \text{m}^2/\text{s}^2 \]

8. **Perform the Calculation:**
Now, substitute and calculate:
\[ T = \frac{3.61201 \times 10^7 \cdot 4 \times 10^{-3}}{3 \cdot 8.31} \]
\[ = \frac{144480400}{24.93} \]
\[ \approx 5795443.241 \, \text{K} \]

9. **Final Result:**
The estimated surface temperature of the Sun is approximately:
\[ T \approx 5795 \, \text{K} \]

### Final Answer:
The surface temperature of the Sun is approximately **5795 K**.