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Set 57 Problem number 19


Problem

A hypothetical atom with negligible kinetic energy has a mass of 223 amu. It undergoes a gamma decay. The remaining atom has atomic mass which is less than that of the original by .0000174 amu. What is the kinetic energy and/or wavelength (whichever is more appropriate) of the emitted particle, assuming that the kinetic energy of the remaining atom is negligible? How much energy would be released by the decay of a mole of these atoms? Note that the mass of a helium nucleus is about 4.001 amu and the mass of an electron about .00055 amu, where an amu is approximately 1.66 * 10^-27 kg?

Solution

In a beta decay all the energy released is carried away in a photon--there is no massive particle involved. This energy corresponds to a change in the 'orbit' of a particle in the nucleus, and is analogous to the effect of a change in the orbital of an electron.

The energy therefore corresponds to the entire .0000174 kg of mass lost:

The wavelength of this photon is found from the relationship E = h f = h c / `lambda to be

A mole of these nuclei would constitute 6.02 * 10^23 nuclei, each releasing 25.9956 * 10^-16 Joules. The total energy released would therefore be

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