The reaction energy of a reaction is the amount of energy released by the reaction. It is found by determining the difference in mass between the reactants and products and then using E=mc2 to convert the lost mass into the released energy. Look again at the equation for the decay of radium (Ra), given in the introduction. Use the following table of masses to determine the reaction energy of this reaction.Nucleus or particle Mass in atomic mass unitsradium-226 226.025402radon-222 222.017571alpha particle 4.002602Express your answer in joules to three significant figures.

Use Energy Conservation. By ``alpha decay converts'', we mean that the parent particle turns into an alpha particle and daughter particles. Adding the mass of the alpha and daughter radon, we get

m = 4.00260 u + 222.01757 u = 226.02017 u .

The parent had a mass of 226.02540 u, so clearly some mass has gone somewhere. The amount of the missing mass is

Delta m = 226.02540 u - 226.02017 u = 0.00523 u ,

which is equivalent to an energy change of

Delta E = (0.00523 u)*(931.5MeV/1u)

Delta E = 4.87 MeV

Converting 4.87 MeV to Joules

1 joule [J] = 6241506363094 mega-electrón voltio [MeV]

4 mega-electrón voltio = 6.40870932 x 10^(-13) joule

4.87 mega-electrón voltio = 7.8026035971 x 10^(-13) joule

snehashish65 snehashish65 · Answer 2 · 2021-12-10T06:43:32+01:00

The required amount of energy released due to loss of mass is [tex]7.80 \times 10^{-13} \;\rm J[/tex].

Given data:

Einstein's mass - energy relation is given as, [tex]E = mc^{2}[/tex].

Here,

m is the mass and c is the speed of light.

Use Energy Conservation. By ``alpha decay converts'', we mean that the parent particle turns into an alpha particle and daughter particles. Adding the mass of the alpha and daughter radon, we get

m = 4.00260 u + 222.01757 u

m = 226.02017 u .

The parent had a mass of 226.02540 u, so clearly some mass has gone somewhere. The amount of the missing mass is,

[tex]\Delta m = 226.02540\;\rm u - 226.02017\;\rm u\\\\\Delta m = 0.00523 \;\rm u[/tex]

Then the equivalent change in the energy is given as,

[tex]\Delta E = (0.00523 \;\rm u) \times (931.5\;\rm MeV/u)\\\Delta E = 4.87 \;\rm MeV[/tex]

Converting 4.87 MeV to Joules as,

[tex]1 \;\rm J= 6.242 \times 10^{12}\;\rm MeV\\4.87 \;\rm MeV = \dfrac{4.87}{ 6.242 \times 10^{12}}\;\rm J\\\\ =7.80 \times 10^{-13} \;\rm J[/tex]

Thus, we can conclude that the required amount of energy released due to loss of mass is [tex]7.80 \times 10^{-13} \;\rm J[/tex].

Learn more about the Equivalent energy here:

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