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## Homework Statement

A 67-Zn nucleus is at rest and in its first excited state, 93.3 keV above the ground state. The nucleus then decays to the ground state with the emission of a gamma ray. (One atomic mass unit is 931.5 MeV/c2.) What is the recoil speed of the nucleus? (You can assume non-relativistic motion, if needed.)

## Homework Equations

K

_{z}=P

_{z}

^{2}/2m

E

_{g}=P

_{g}c

E

_{g}+K

_{z}=93.3 keV

Where P

_{z}=P

_{g}in magnitude

## The Attempt at a Solution

There's no point for me to type everything I did, but I'll describe it. I solved for P

^{2}in each equation and set them equal to each other:

K

_{z}2m=E

_{g}

^{2}/c

^{2}

then I used E

_{g}+K

_{z}=93.3 keV to substitute and I attempted to solve using the quadratic equation. However, a few times now I've gotten the K

_{z}to be greater than 93.3keV by itself, which is obviously not right.