You must show how to get answer!!!! The beta-decay of 24Na produces a 24Mg nucle

Question

You must show how to get answer!!!!

The beta-decay of 24Na produces a 24Mg nucleus in an excited state. The magnesium nucleus then gamma-decays to its ground state by emission of a 1.369-MeV gamma ray. Assuming the nucleus is at rest immediately before the gamma decay, find the velocity of the 24Mg nucleus after emission of the gamma ray. The mass of the nucleus is in Appendix A of the OpenStax textbook. You will need to use conservation of momentum, from our first term of physics! (Hint: since the gamma-ray energy is so low compared to the mass energy of the nucleus, we do not need to use a relativistic expression for the momentum of the nucleus. This simplifies the algebra greatly.) Keep three significant digits.

Explanation / Answer

Energy released during gamma radiation = 1.369 Mev

Momentum of gamma ray = E/c = 1.369*(10^6)/3*(10^8) = 4.56*(10^ -3)

= 4.56*(10^ -3)*1.6*(10^ -19) = 7.296*(10^ -22)

This is equal to momentum of 24Mg

MASS of 24Mg = 24 amu = 24*1.67*(10^-27)

m*v = 7.296*(10^ -22)

V = 1.82*(10^4) m/s

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