Nuclei

It is the equation of neutron (n) decays into a proton (p), in which an electron (e⁻) is emitted, and an antineutrino is emitted to conserve lepton number.

Binding energy per nucleon of deuteron \( \left(^2_1\text{H}\right) = 1.1\, \text{MeV} \)
Binding energy per nucleon of helium-4 \( \left(^4_2\text{He}\right) = 7.0\, \text{MeV} \)

Two deuterons \( \Rightarrow \) total nucleons = 2 × 2 = 4

\[
\text{BE}_{\text{reactants}} = 2 \times (1.1 \times 2) = 4.4\, \text{MeV}
\]

\[
\text{BE}_{\text{product}} = 4 \times 7.0 = 28.0\, \text{MeV}
\]

\[
Q = \text{BE}_{\text{product}} - \text{BE}_{\text{reactants}} = 28.0 - 4.4 = \boxed{23.6\, \text{MeV}}
\]

The binding energy per nucleon for this nucleus is $\frac{21}{7}=3u$

The term Isotones refers to nuclides (atoms of different elements) that have the same number of neutrons (\(\mathbf{N}\)) but a different number of protons (\(\mathbf{Z}\)).

In a nucleus, the potential energy between two nucleons is lowest at a distance of roughly 0.8 fm . The force turns repulsive as the distance decreases.

The term Isotones refers to nuclides (atoms of different elements) that have the same number of neutrons (\(\mathbf{N}\)) but a different number of protons (\(\mathbf{Z}\)).

The number of remaining nuclei after time t can be given by:

$N\left(t\right)=N_0{e}^{-\lambda t}$

For half-life $t_{1/2}$ of $n_1$, we know that:

$t_{1/2}=\frac{\ln 2}{{\lambda }_1}$

At the end of one half-life, the number of $n_1$ nuclei left will be:

$N_1=\frac{N_0}{2}$

For nucleus $n_2$, which has a decay constant 3 times that of $n_1$ the remaining number of nuclei will be:

$N_2=N_0{e}^{-3}{\lambda }_{1}t$

Since $t=t_{1/2}=\frac{\ln 2}{{\lambda }_1}$, we substitute it into the equation for $N_2$ :

$N_2=N_0{e}^{-3{\lambda }_1\times \frac{\ln 2}{{\lambda }_1}}=N_0{e}^{-3\ln 2}=N_0{\left(\frac{1}{2}\right)}^3=\frac{N_0}{8}$

Now, the ratio of the number of nuclei of $n_2$ to $n_1$ after one half-life of $n_1$ is:

$\frac{N_2}{N_1}=\frac{\frac{N_0}{8}}{\frac{N_0}{2}}=\frac{1}{4}$

The term Isotones refers to nuclides (atoms of different elements) that have the same number of neutrons (\(\mathbf{N}\)) but a different number of protons (\(\mathbf{Z}\)).

A) They are stronger than Coulomb forces.
True — Nuclear forces are much stronger than electrostatic (Coulomb) forces between protons.

(B) They have about the same magnitude for different pairs of nucleons (n–n, p–p, n–p).
True — Nuclear forces are approximately charge-independent.

(C) They are always attractive.
Not true — At very small distances (below about 0.5 fm), nuclear forces become repulsive to prevent nucleons from collapsing into each other.

(D) They saturate as the separation between two nucleons increases.
True — Each nucleon interacts only with nearby ones; the force has a short range and saturates.

C) They are always attractive.​

In a nucleus, the potential energy between two nucleons is lowest at a distance of roughly 0.8 fm . The force turns repulsive as the distance decreases.

Convert mass to kilograms:\(m=1\,\text{g}=1\times 10^{-3}\,\text{kg}\)

Square the speed of light:\(c^{2}=(3\times 10^{8}\,\text{m/s})^{2}=9\times 10^{16}\,\text{m}^{2}/\text{s}^{2}\)

Calculate the energy:\(E=m\times c^{2}=(1\times 10^{-3}\,\text{kg})\times (9\times 10^{16}\,\text{m}^{2}/\text{s}^{2})=9\times 10^{13}\,\text{J}\) Other Units The energy can also be expressed in other units:

Approximately \(2.5\times 10^{7}\) kilowatt-hours (kWh).Approximately \(5.6\times 10^{26}\) mega-electron volts (MeV).

Convert mass to kilograms:\(m=1\,\text{g}=1\times 10^{-3}\,\text{kg}\)

Square the speed of light:\(c^{2}=(3\times 10^{8}\,\text{m/s})^{2}=9\times 10^{16}\,\text{m}^{2}/\text{s}^{2}\)

Calculate the energy:\(E=m\times c^{2}=(1\times 10^{-3}\,\text{kg})\times (9\times 10^{16}\,\text{m}^{2}/\text{s}^{2})=9\times 10^{13}\,\text{J}\) Other Units The energy can also be expressed in other units:

Approximately \(2.5\times 10^{7}\) kilowatt-hours (kWh).Approximately \(5.6\times 10^{26}\) mega-electron volts (MeV).

$n\to P+\overline{e}+\overline{v}$

The term Isotones refers to nuclides (atoms of different elements) that have the same number of neutrons (\(\mathbf{N}\)) but a different number of protons (\(\mathbf{Z}\)).

In a nucleus, the potential energy between two nucleons is lowest at a distance of roughly 0.8 fm . The force turns repulsive as the distance decreases.