To convert the speed of the helium atom from meters per second (m/s) to miles per hour (mph), we can use the conversion factors:
1 mile = 1609 meters and there are 3600 seconds in an hour.
The conversion from m/s to mph can be done as follows:
\[ \text{Speed in mph} = \text{Speed in m/s} \times \frac{3600 \text{ seconds}}{1 \text{ hour}} \times \frac{1 \text{ mile}}{1609 \text{ meters}} \]
Substituting the given speed of 1210 m/s:
\[ \text{Speed in mph} = 1210 , \text{m/s} \times \frac{3600 , \text{s}}{1 , \text{hour}} \times \frac{1 , \text{mile}}{1609 , \text{meters}} \]
Now, let's calculate it step by step:
-
Calculate \( \frac{3600}{1609} \): \[ \frac{3600}{1609} \approx 2.237 \]
-
Now multiply that by 1210 m/s: \[ \text{Speed in mph} = 1210 , \text{m/s} \times 2.237 \approx 2707.07 , \text{mph} \]
-
Since the initial value (1210) has three significant figures, we should round our final result to three significant figures as well.
Thus, rounding 2707.07 to three significant figures gives:
\[ \text{Speed in mph} \approx 2710 , \text{mph} \]
Therefore, the speed of the helium atom in miles per hour is 2710 mph.