One Atomic Mass Unit

solved MassEnergy

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

Inputs

mass

m

1 u

Outputs

energy

E

How it's solved

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 web of concepts

given read from the words equation asked

The Ruby that solves it

The question and its solution are small Ruby files. The engine runs them.

question.rb

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

solution.rb

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

playground.rb

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

The laws it drew on

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)