Substitute the values from the exercise for E and m in the given formula. Then, use square roots to find the speed of light. Remember to check if the answer is written in scientific notation.
3 * 10^8 meters per second
Practice makes perfect
We want to find the speed of light using Albert Einstein's formula and information about a hydrogen atom. First, let's take a look at the famous equation created by Einstein.
E=mc^2In this formula, E is the energy of an object in joules, m is the mass of the object in kilograms, and c is the speed of light in meters per second. We will start our calculations by rewriting the equation a bit so that it will be easier for us to find the speed of light.
E=mc^2 ⇕ c^2=E/m
From the exercise, we know that a hydrogen atom has 15.066 * 10^(-11) joule of energy and a mass of 1.674 * 10^(-27) kilogram. Let's substitute 15.066 * 10^(-11) for E and 1.674 * 10^(-27) for m in the equation and solve for c. Notice that c is squared in the equation, which means that we need to take the square root of the equation to find its value. Let's do it!
We found that the speed of light is about 3 * 10^8 meters per second. The answer is already in scientific notation, so we do not have to rewrite it. Note that we do not need to consider the negative root because speed cannot be negative.
