Problem 25 - Chemistry: An Atoms-Focused Approach

Question

Speed of Light How long does it take light to reach Earth from the sun when the distance between them is 149.6 million kilometers?

Step-by-Step Solution

Answer

Answer: Approximately 499.0 seconds.

Step 1: Convert distance to kilometers

First, ensure that the distance between the sun and the Earth is in kilometers. In this case, it is already given in kilometers (149.6 million), so no conversion is needed.

Step 2: Identify the speed of light

The speed of light, denoted as "c", is approximately 299,792 kilometers per second. We will use this value to find the time it takes for light to travel from the sun to the Earth.

Step 3: Set up the formula to find the time

To find the time it takes for light to travel from the sun to the Earth, we'll use the formula: time = distance / speed, where time is what we want to find, distance is the distance between the sun and Earth, and speed is the speed of light. So, we'll have: time = (149.6 million kilometers) / (299,792 kilometers per second)

Step 4: Perform the calculation

Now, we just need to divide the distance (149.6 million kilometers) by the speed of light (299,792 kilometers per second) to find the time it takes for light to travel from the sun to the Earth: time = (149,600,000 kilometers) / (299,792 kilometers per second) = 499.00976 seconds

Step 5: Round the answer to an appropriate number of significant figures

Since the distance is given with 4 significant figures, we'll round our answer to the same level: time ≈ 499.0 seconds So, it takes approximately 499.0 seconds for light to reach Earth from the sun.

Key Concepts

Distance Conversion

When working with distances in physics, it is crucial to ensure that all measurements are in the correct units before performing any calculations. This is called distance conversion. Often in exercises, distances might be given in kilometers, meters, or even miles, depending on where you source the data. In our original exercise, the distance from the sun to Earth is presented as 149.6 million kilometers. Thankfully, it's already in the standard unit for our problem, so we don't need any conversion.

If conversion were needed, for example from miles to kilometers, you would multiply the distance in miles by 1.60934 since one mile equals approximately 1.60934 kilometers. The key is to understand what unit your answer must be in and to ensure all input measurements are converted to that unit before proceeding.

Speed Calculation

Speed calculation is a critical aspect of many physics problems. It involves determining how quickly an object travels a set distance. Generally, speed is the rate at which someone or something moves or operates and it’s usually given in units like meters per second or kilometers per hour.

In this exercise, we look at the speed of light, a constant typically denoted as "c" and valued at roughly 299,792 kilometers per second. To find out how long light takes to travel from the sun to Earth, we use the speed calculation formula: \[\text{time} = \frac{\text{distance}}{\text{speed}}\] With this, you divide the total distance (from the sun to the Earth) by the speed (of light) to get the time. For our example, the calculation would be: \[\text{time} = \frac{149,600,000 \text{ km}}{299,792 \text{ km/s}} \]which simplifies to approximately 499 seconds. This calculation is fundamental in determining various travel times and helps us better understand the movement of different entities across space.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. This concept is critical in scientific calculations to accurately report the precision of calculated results.

In practical terms, using significant figures means you consider the precision of the instruments you're working with. For instance, the distance from the sun to Earth is given with four significant figures in the problem (149.6 million kilometers). The speed of light itself, 299,792 kilometers per second, is also an exact scientific number often used in calculations.
After performing calculations, it's important to round your answer to reflect the precision of the initial figures. In this problem, our result of 499.00976 seconds should be rounded to four significant figures, yielding 499.0 seconds, to match the initial distance’s precision. This way, we maintain consistency and communicate the level of accuracy related to the initial data.