The glow-in-the-dark dials on some watches and some keychain lights shine with e

Question

The glow-in-the-dark dials on some watches and some keychain lights shine with energy provided by the decay of radioactive tritium, 31H. 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 17 MBq .

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

Part B: What is the power, in watts, provided by the radioactive decay process?

Explanation / Answer

Solution:

a) E=0.5mev2

(19000)(1.602x10-19)J=0.5(9.109x10-31)v2

v=8.17x107m/s

b) W = EA/M

M=3g/mole

A/M = kN0/M

k=ln2/(12)(3.1536x107sec)

= 1.83x10-9s-1

A = 17x106Bq

W = ((19000)(1.602x10-19))(17x106)/(3)

= 1.72x10-8W

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