Mathematics I / Introduction to Modern Physics
Practice question · Numerical answer

Take the speed of light as 3 x 10^8 m/s. Fully converting 2 kg of matter to energy gives E = 1.8 x 10^n joules. Enter the value of n.

Hints
  1. Square the speed of light first: the exponent doubles.
  2. c squared is 9 x 10^16, and 2 times 9 is 18, which must be rewritten as 1.8 x 10.
Show the answer

17

Why

c2=9×1016c^{2} = 9 \times 10^{16}, so E=2×9×1016=18×1016=1.8×1017E = 2 \times 9 \times 10^{16} = 18 \times 10^{16} = 1.8 \times 10^{17} J. The renormalisation from 18 to 1.8 bumps the exponent by one, a step routinely dropped, giving 16. The enormous size of the number is why a tiny mass powers a reactor.

Read the lesson: Introduction to Modern Physics →

Practise Introduction to Modern Physics

The app has 6 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.

More questions on Introduction to Modern Physics