# Calculate the mass deficit in this nuclear reaction

#### subarua

Calculate the mass deficit in this nuclear reaction

$12{\rm C}+\frac{12}{6}{\rm C}\rightarrow \frac{24}{12}{\rm Mg}$

Information given:

- rest mass of a carbon-12 nucleus: $1.9921157\times 10^{-26}\,{\rm kg}$

- rest mass of a magnesium nucleus: $3.9817469\times 10^{-26}\,{\rm kg}$

- rest mass of a proton: $1.67353\times 10^{-27}\,{\rm kg}$

- rest mass of a neutron: $1.67492\times 10^{-27}\,{\rm kg}$

- speed of light: $3.00\times 10^{8}\,{\rm m}\,{\rm s}^{-1}$

My attempts so far haven't been great I'm thinking along the line of using a formula but even then I don't know what variables to plug in where.

thanks

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#### MrIknowitall

this can be easily solved: $1.9921157×10^−26kg+1.9921157×10^−26kg-3.981746×10^−26kg=0.0024845×10^−26kg$

#### benit13

$$\displaystyle \Delta m = 3.9817469\times 10^{-26} - 2 (1.9921157\times 10^{-26}) = - 0.0024845 \times 10^{-26} = -2.4845 \times 10^{-29} kg = -13.937 MeV/c^2$$

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#### Woody

Is this a correct interpretation?

I am unfamiliar with the notation used by subarua.
However I guess that 12/6 against the Carbon indicates Carbon 12 with 6 protons (thus also 6 neutrons)
and similarly 24/12 indicates Magnetism 24 with 12 protons (and 12 neutrons)

Or perhaps the notation indicates Carbon 12 with 6 neutrons...

Either way this would then suggest that the original equation provided should have both carbons preceded by 12/6.

• 1 person

#### benit13

I am unfamiliar with the notation used by subarua.
However I guess that 12/6 against the Carbon indicates Carbon 12 with 6 protons (thus also 6 neutrons)
and similarly 24/12 indicates Magnetism 24 with 12 protons (and 12 neutrons)

Or perhaps the notation indicates Carbon 12 with 6 neutrons...

Either way this would then suggest that the original equation provided should have both carbons preceded by 12/6.
Yeah it's

$$\displaystyle ^{12}_{6}C + ^{12}_{6}C = ^{24}_{12}Mg$$,

but it's typical to leave out the atomic number since you can identify that from the element, so reactions are typically stated using

$$\displaystyle ^{12}C + ^{12}C = ^{24}Mg$$

or in the nucleosynthesis literature:

$$\displaystyle ^{12}C(^{12}C, \gamma) ^{24}Mg$$

• 2 people