Mass/charge balance of Beta decay/nuclear reactions

[cashmoney805]

Homework Statement

There are three different reactions we did in class.
B-: ₆C¹⁴ --> ₇N¹⁴ + e-
B+: ₆C¹¹ --> ₅B₁₁ + e+
Nuclear rxn: alpha particle + ₇N¹⁴ --> ₈O¹⁷ + e+

Homework Equations

Q tot = (mass inital - mass final) * 931.5 MeV
Charge balance

The Attempt at a Solution

In class, for B- the teacher wrote down:
Q= (Mass of C nucleus) - (mass of N nucleus) - 1 e-
= (mass of C atom - 6 e-) - (mass of N atom - 7 e-) - (mass of 1 e-)
so -6 -(-7) - 1 = 0 so Q= (mass of C atom) - (mass of N atom)

B+
Q = (mass of C nuc) - (Mass of B nuc) - (mass of e+)
Q= (mass of C atom - 6 e-) - (mass of B atom - 5 e-) - mass of 1 e-
Q= -6 -(-5) -1 = -2, so he said Q total = (mass of C) - (mass of B + 2e-)

Nuclear rxn
Q = (mass of alpha nuc) + (mass of N nuc) - (mass of O nuc) - (mass of e+)
Q = (mass of He - 2 e-) + (mass of N atom - 7 e-) - (mass of O atom - 8 e-) - (mass of e+)
Q = -2 + -7 - (-8) -1 = -2 e-
However, he said in class that the Q = (mass of alpha particle + mass of N atom) - (mass of O atom)
Can someone please clear this up for me? I really don't get the charge/mass balance. Thanks so much

 

[RoryP]

so basically you have to make sure that the mass and charge is the same before the reaction as it is after.
remember energy can't be created, it simply changes from one form to another =]
and also for B- emission you would have an anti-electron-neutrino and for B+ emission you would have an electron-neutrino!

 

[nlightner]

!

I would like to clarify the concept of mass/charge balance in beta decay and nuclear reactions. In these reactions, the total mass and charge of the reactants must be equal to the total mass and charge of the products, according to the law of conservation of mass and charge.

In the first reaction, B-, the mass balance equation is correctly written as (mass of C nucleus) - (mass of N nucleus) - (mass of 1 e-). This is because the reactant (C14) has a mass of 14 atomic mass units (amu) and a charge of 6 (6 protons and 6 electrons), while the products (N14 + e-) have a combined mass of 14 amu and a charge of 7 (7 protons and 7 electrons). The mass balance is achieved by subtracting the mass of the electron from both sides, as electrons have a negligible mass compared to protons and neutrons. The charge balance is achieved by taking into account the additional electron in the products.

In the second reaction, B+, the mass balance equation is also correct as (mass of C nucleus) - (mass of B nucleus) - (mass of 1 e+). However, the charge balance equation is not completely accurate. The correct equation should be (charge of C nucleus) - (charge of B nucleus) + (charge of 1 e+). This is because, in B+ decay, a positron (e+) is emitted, which has a positive charge of 1. Therefore, the charge balance equation should take into account the additional positive charge in the products.

In the third reaction, the nuclear reaction, the mass balance equation is correctly written as (mass of alpha particle) + (mass of N nucleus) - (mass of O nucleus) - (mass of 1 e+). However, the charge balance equation is not accurate. The correct equation should be (charge of alpha particle) + (charge of N nucleus) - (charge of O nucleus) + (charge of 1 e+). This is because, in this reaction, a positron is emitted along with the alpha particle and the products have a different charge than the reactants.

It is important to note that the equations for mass and charge balance may vary depending on the specific reaction being studied. It is always important to carefully consider the charges and masses of each particle involved in the reaction to accurately balance