Behind the last lesson's enormous exchange rate sits one short equation. This lesson writes it down, names each symbol with its unit, and shows what makes the rate so steep.
In the electromagnetic waves topic, you met the speed of light in a vacuum: light crosses empty space at 3.00 × 10⁸ m/s, and the symbol for that speed is c. The same c is about to appear in an equation about mass.
E is the energy equivalent of the mass, measured in joules (J).
m is the mass, measured in kilograms (kg).
c is the speed of light in a vacuum, the same 3.00 × 10⁸ m/s at which light crosses empty space.
The conversion factor is c², the speed of light multiplied by itself.
Here is why the exchange rate is so steep: because the conversion factor c² is enormous (about 9 × 10¹⁶ joules per kilogram of mass), a tiny amount of mass is equivalent to a huge amount of energy.
With c² so large, even the brick's single kilogram from the first lesson is equivalent to an enormous number of joules.
A classmate writes E = mc² and asks Caspian what each symbol stands for. What should Caspian say?
E is the energy equivalent of the mass, in joules.
m is the mass, in kilograms.
c is the speed of light in a vacuum, 3.00 × 10⁸ m/s.
E is the energy equivalent in joules, m is the mass in kilograms, and c is the speed of light in a vacuum, 3.00 × 10⁸ m/s.
A speck with a mass of 1.0 × 10⁻¹¹ kg is fully converted to energy. Use E = mc², with c = 3.00 × 10⁸ m/s, to find the energy released.
Write down the values:
m = 1.0 × 10⁻¹¹ kg, c = 3.00 × 10⁸ m/s, E = ?
Write down the equation:
E = mc²
Substitute in the values, and calculate:
E = (1.0 × 10⁻¹¹) × (3.00 × 10⁸)². Squaring c gives 9.00 × 10¹⁶. Then 1.0 × 9.00 = 9.00, and the powers of ten make 10⁵. So E = 9.0 × 10⁵ J.
The energy released is 9.0 × 10⁵ J.
Delphine measures a pebble's mass in kilograms. Which quantity does E = mc² let her calculate from that mass?
Mireille says: 'The c in E = mc² is the same speed at which light crosses empty space, 3.00 × 10⁸ m/s.' Is Mireille correct?
Why is a tiny mass equivalent to a huge energy?
Which set of units belongs to the quantities in E = mc²?
About how many joules of energy are equivalent to one kilogram of mass?
A dust grain loses 7.0 × 10⁻¹³ kg of mass, all of it converted to energy. Use E = mc², with c = 3.00 × 10⁸ m/s, to calculate the energy released, in joules, to two significant figures.