Beta decay problems, not getting the right answer

In summary, the energy of the neutrino is calculated by subtracting the mass of the product atom from the mass of the original atom, converting it to energy using the equation E=mc^2, and then subtracting the kinetic energy of the accompanying electron. The maximum kinetic energy of the emitted electron is calculated by subtracting the mass of the product atom from the mass of the original atom and converting it to energy. The energy of the electron neutrino is calculated by subtracting the mass of the product atom from the mass of the original atom, converting it to energy, and then subtracting the energy of the emitted positron. The mass of the emitted electrons comes from the difference in mass between the original atom and the product atom
  • #1
crosbykins
53
0

Homework Statement



a) What is the energy of the neutrino, if a phosphorus-32 atom (31.97390
u) beta-decays into a sulphur-32 atom (31.97207 u), and the kinetic energy of the
accompanying electron is 0.90 MeV? (answer: 0.25 MeV)

b) A boron-12 atom (12.01435 u) beta-decays into a carbon-12 atom (12.00000 u).
What is the maximum kinetic energy of the emitted electron? (answer: 12.8 MeV)

c) In the β+ decay of nitrogen-12 (12.01864 u) into carbon-12 (12.00000 u), a
positron with energy of 11.0 MeV is emitted. What is the energy of the electron
neutrino? (answer: 5.8 MeV)



Homework Equations



** equations not really used

The Attempt at a Solution



a)

Δ m = 31.97390u – 31.97207u
= 1.83*10^-3 u

(1.83*10^-3 u) (931 MeV)
= 1.70 MeV

1.70 MeV – 0.90MeV
=.80 MeV

Therefore, the energy of the neutrino is .80 MeV.

b)
Δ m = 12.01435u – 12.00000u
= .01435u

(.01435u)( 931 MeV)
=13 MeV

Therefore, the maximum kinetic energy is 13 MeV.

c)

Δ m = 12.01864u - 12.00000u
= .01864u

(.01864u) ( 931 MeV)
=17 MeV

17 MeV – 11.0MeV
= 7MeV

Therefore, the energy of the neutrino is 7MeV.

***right, so the answers i got are all wrong, i think the method in which I'm doing this is wrong, but i can't find information in my book on how to do it the correct way... a step-by-step solution would really really be appreaciated, thanks :)
 
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  • #2
Where does the mass of the emitted electrons come from?
 

Related to Beta decay problems, not getting the right answer

1. What is beta decay and why is it important?

Beta decay is a type of radioactive decay where an unstable atomic nucleus emits a beta particle (either an electron or a positron) in order to become more stable. This process helps to maintain the balance of protons and neutrons in the nucleus and plays a crucial role in the natural decay of elements.

2. Why am I not getting the right answer when solving beta decay problems?

There could be several reasons for not getting the right answer when solving beta decay problems. One common mistake is not properly accounting for the mass and energy of the particles involved. Another possibility is using incorrect equations or not understanding the concept of half-life. It is important to double check all calculations and seek help from a tutor or professor if needed.

3. How do I know which type of beta decay is occurring in a specific nucleus?

The type of beta decay that occurs in a nucleus depends on the ratio of protons to neutrons. If there are more protons than neutrons, beta minus decay (emitting an electron) will occur. If there are more neutrons than protons, beta plus decay (emitting a positron) will occur. Additionally, electron capture (absorbing an electron) can also occur in certain nuclei.

4. Can beta decay ever be reversed?

No, beta decay is a natural process that cannot be reversed. However, in some cases, a nucleus can undergo beta capture, where a proton is absorbed and a neutron is emitted, effectively reversing the process of beta decay.

5. How is beta decay used in practical applications?

Beta decay has many practical applications, including nuclear power generation, radiocarbon dating, and medical imaging. It is also used in industrial processes such as controlling the thickness of materials and detecting the presence of small amounts of radioactive substances.

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