Part Problem VII.14 The glow-in-the-dark dials on some watches and some keychain

Question

Part Problem VII.14 The glow-in-the-dark dials on some watches and some keychain lights shine with energy provided by the decay of radioactive tritium, 3^1H. Tritium is a radioactive isotope of hydrogen with a half-life of 12 years. Each decay emits an electron with an energy of 19 KeV. A typical new watch has tritium with a total activity of 21MBq. Part A What is the speed of the emitted electron? (This speed is high enough that you’ll need to do a relativistic calculation.) include units Part B What is the power, in watts, provided by the radioactive decay process? include units Part C What will be the activity of the tritium in a watch after 7 years, assuming none escapes? Part Problem VII.14 The glow-in-the-dark dials on some watches and some keychain lights shine with energy provided by the decay of radioactive tritium, 3^1H. Tritium is a radioactive isotope of hydrogen with a half-life of 12 years. Each decay emits an electron with an energy of 19 KeV. A typical new watch has tritium with a total activity of 21MBq. Part A What is the speed of the emitted electron? (This speed is high enough that you’ll need to do a relativistic calculation.) include units Part B What is the power, in watts, provided by the radioactive decay process? include units Part C What will be the activity of the tritium in a watch after 7 years, assuming none escapes? The glow-in-the-dark dials on some watches and some keychain lights shine with energy provided by the decay of radioactive tritium, 3^1H. Tritium is a radioactive isotope of hydrogen with a half-life of 12 years. Each decay emits an electron with an energy of 19 KeV. A typical new watch has tritium with a total activity of 21MBq. Part A What is the speed of the emitted electron? (This speed is high enough that you’ll need to do a relativistic calculation.) include units Part B What is the power, in watts, provided by the radioactive decay process? include units Part C What will be the activity of the tritium in a watch after 7 years, assuming none escapes? Part A What is the speed of the emitted electron? (This speed is high enough that you’ll need to do a relativistic calculation.) include units Part B What is the power, in watts, provided by the radioactive decay process? include units Part C What will be the activity of the tritium in a watch after 7 years, assuming none escapes? What will be the activity of the tritium in a watch after 7 years, assuming none escapes?

Explanation / Answer

Part A What is the speed of the emitted electron? (This speed is high enough that you’ll need to do a relativistic calculation.) include units

K = (1/(1 - v^2)^0.5 - 1) m c^2
19e3 = (1/(1 - v^2)^0.5 - 1) 0.510 998 910e6 ==> v = 0.265c = 0.80 x 10^8 m/s

Part B What is the power, in watts, provided by the radioactive decay process? include units
21e6 * 19e3 eV * 1.6e-19 J/eV = 6.388 * 10^-8 W

Part C What will be the activity of the tritium in a watch after 7 years, assuming none escapes?
A = N/N0 A0 = (0.5^(t/T)) A0 = (0.5^(7/12)) * 21e6 = 14 x 10^6 Bq

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