NapkinCalc

Physics 5 — Modern Physics

E = mc² and half-life

continues from lesson 4 — values defined earlier in the course stay live here

Mass is frozen energy at an outrageous exchange rate. One gram, fully converted:

Egram=0.001cl2E_{gram} = 0.001 \cdot c_{l}^{2} = 8.988×10138.988 \times 10^{13} ~9×10¹³ J — a city's daily electricity, from a paperclip

Unstable nuclei cash that energy out randomly but statistically on schedule: half are gone every half-life. Carbon-14 (t½ = 5730 y) turns every old object into a clock:

100 * 0.5^(x / 5730)
20406080100050001000015000200002500030000

C-14 remaining (%) vs age (years) — measure the fraction, read off the age

✓ pass abs(1000.55730573050)<109\mathrm{abs}\left(100 \cdot 0.5^{\frac{5730}{5730}} - 50\right) < 10^{-9} one half-life, half remains — by definition

That closes the Physics track: motion, momentum, fields, heat, and the modern rules underneath them all.