# A-level Physics (Advancing Physics)/Half-lives/Worked Solutions

**1. Radon-222 has a decay constant of 2.1μs ^{-1}. What is its half-life?**

**2. Uranium-238 has a half-life of 4.5 billion years. How long will it take for a 5 gram sample of U-238 to decay to contain 1.25 grams of U-238?**

2 half-lives, since 1.25 is a quarter of 5. 2 x 4.5 = 9 billion years.

**3. How long will it be until it contains 0.5 grams of U-238?**

First calculate the decay constant:

**4. Tritium, a radioisotope of Hydrogen, decays into Helium-3. After 1 year, 94.5% is left. What is the half-life of tritium (H-3)?**

(if λ is measured in yr^{-1})

**5. A large capacitor has capacitance 0.5F. It is placed in series with a 5Ω resistor and contains 5C of charge. What is its time constant?**

**6. How long will it take for the charge in the capacitor to reach 0.677C? ()**

2 x τ = 5s