One Atomic Mass Unit

Q. What is the energy equivalent of 1 u, in MeV? expects 931.5 MeV

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The web of concepts

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Q. What is the energy equivalent of 1 u $m = 1$ u, in MeV?

The playground

Inputs

mass

m

1 u

Outputs

energy

E

The solution

Solved with MassEnergy

Given

$m = 1$ u

Find $E$ .

Working

$m = 1$ u $= 1.66053907 \times 10^{−27}$ kg
einsteins mass energy(nucleon) $E = m \cdot c^{2}$
$E = 1.66053907 \times 10^{−27} \cdot {(2.99792458 \times 10^{8})}^{2}$
$E = 931.5$ MeV
$E = 1.49241809 \times 10^{−10}$ J $= 931.494102$ MeV
$E \approx 931.5$ MeVto 4 significant figures

Conclusion

An atomic mass unit is worth nearly a thousand MeV, so nuclear masses and nuclear energies can be counted in the same units.

The Ruby

1require_relative "../physics"23question :one_atomic_mass_unit do4  kind :numerical5  describes "%{energy} of %{mass}, in MeV?"6  given mass: "1 u"7  asks energy: "What is the energy equivalent"8end

1require_relative "../questions/one_atomic_mass_unit"2require_relative "../science/nuclei/mass_energy"34solve :one_atomic_mass_unit, using: MassEnergy do5  objects :nucleon67  take mass: nucleon.mass89  energy = nucleon.energy10  answer energy:, in: "MeV", figures: 41112  conclusion "An atomic mass unit is worth nearly a thousand MeV, so nuclear masses and nuclear energies can be " \13             "counted in the same units."14end

1require_relative "../solutions/one_atomic_mass_unit"23play_with :one_atomic_mass_unit do4  title "One Atomic Mass Unit"5end

The laws

quantity	written	units	within	from
speed of light	$c$	m/s	—	MassEnergy
hydrogen atom mass	$m_{H}$	kg	—	MassEnergy
neutron mass	$m_{n}$	kg	—	MassEnergy
mass	$m$	kg	0 … ∞	MassEnergy
energy	$E$	J	—	MassEnergy
atomic number	$Z$	—	—	MassEnergy
mass number	$A$	—	0 … ∞	MassEnergy
mass defect	$dm$	kg	—	MassEnergy
binding energy	$E_{b}$	J	—	MassEnergy
q value	$Q$	J	—	MassEnergy
energy of ground	$E_{g}$	J	—
mass of ground	$m_{g}$	kg	0 … ∞
energy of nucleon	$E$	J	—
mass of nucleon	$m$	kg	0 … ∞
mass defect of ground	${dm}_{g}$	kg	—
atomic number of ground	$Z_{g}$	—	—
mass number of ground	$A_{g}$	—	0 … ∞
mass defect of nucleon	$dm$	kg	—
atomic number of nucleon	$Z$	—	—
mass number of nucleon	$A$	—	0 … ∞
binding energy of ground	$E_{b,g}$	J	—
binding energy of nucleon	$E_{b}$	J	—
q value of ground	$Q_{g}$	J	—
q value of nucleon	$Q$	J	—

E_{b} = m_{b} \cdot c^{2}

einsteins mass energy

{dm}_{n} = Z_{n} \cdot m_{H} + (A_{n} - Z_{n}) \cdot m_{n} - m_{n}

mass lost in binding

E_{b,n} = {dm}_{n} \cdot c^{2}

energy of the lost mass

Q_{r} = {dm}_{r} \cdot c^{2}

energy a reaction gives out

E_{g} = m_{g} \cdot c^{2}

einsteins mass energy(ground)

E = m \cdot c^{2}

einsteins mass energy(nucleon)

{dm}_{g} = Z_{g} \cdot m_{H} + (A_{g} - Z_{g}) \cdot m_{n} - m_{g}

mass lost in binding(ground)

dm = Z \cdot m_{H} + (A - Z) \cdot m_{n} - m

mass lost in binding(nucleon)

E_{b,g} = {dm}_{g} \cdot c^{2}

energy of the lost mass(ground)

E_{b} = dm \cdot c^{2}

energy of the lost mass(nucleon)

Q_{g} = {dm}_{g} \cdot c^{2}

energy a reaction gives out(ground)

Q = dm \cdot c^{2}

energy a reaction gives out(nucleon)