Physics M.C.Q (1 Marks)

One an amu is $\frac{1}{10}$​ of the mass of one carbon$-12$ atom.
It is equal to $\frac{1}{\text{NA}}$
$\frac{1}{6.022\times10^{23}}$
$= 1.66 \times 10^{-24} \mathrm{~g} $

Sir Einstein's mass$-$energy equation states that mass and energy can be converted into each other by the following relation.
$\mathrm{E}=\mathrm{mc}^2,(\mathrm{c}=\text { speed of light })$
This implies that a small amount of mass contains a lot of energy, which can be proved with an example.
Let we have a mass of $1 \mathrm{~g}=10^{-3} \mathrm{~kg}$, therefore energy produced by it will be:
$E=10^{-3} \times\left(3 \times 10^8\right) 2=9 \times 10^{13} \mathrm{~J}$ which is a vast amount energy produced by only one gram $($small mass$)$ of mass.
Whereas a small amount of energy doesn't give a large amount of mass because for that we have to divide the energy by $\mathrm{c}^2$, which gives a small mass.

Radius of a nucleus with mass number $A$ is given as
$\text{R}=\text{R}_{\text{0}}\text{A}^{\frac{1}{3}}$
Here, $\text{R}_0=1.2\text{fm}$
$\therefore$ Volume of the nucleus $=\frac{4\pi\text{R}^3}{3}=\frac{4\pi\text{R}^3\text{A}}{3}$
This depends on $A.$ With an increase in $A, V$ increases proportionally.
Mass of the nucleus $\simeq\text{Am}_{\text{N}}$
Here, $m_N <$ is the mass of a nucleon.
Therefore, mass of the nucleus also increases with the increasing mass number. Binding energy also depends on mass number $($number of nucleons$)$ as it is the difference between the total mass of the constituent nucleons and the nucleus. Therefore, it also varies with the changing mass number.
On the other hand,
$\text{Density}=\frac{\text{Mass}}{\text{Volume}}$
$=\frac{\text{Am}_{\text{N}}}{\frac{4\pi\text{R}3}{3}}=\frac{\text{Am}_{\text{N}}}{\frac{4\pi\text{R}_0^3\text{A}}{3}}=\frac{\text{m}_{\text{N}}}{\frac{4\pi\text{R}_0^3}{3}}=\frac{3\text{m}_{\text{N}}}{4\pi\text{R}_{0}^3}$
This is independent of $A$ and hence does not change as mass number increases.

In fast chain reaction neutron released in previous fission again strikes $^{235}U$, So size of $^{235}U$ block should be greater than it's critical size.

In nuclear physics, nuclear fusion is a nuclear reaction in which two or more atomic nuclei collide at a very high speed and join to form a new type of atomic nucleus. During this process, matter is not conserved because some of the matter of the fusing nuclei is converted to photons $($energy$).$

$32\text{​P}\\ \ 15$ is the radioactive isotope of phosphorous element.
As it has more number of neutrons than number of protons.

For neutron decay, some mass disappears as neutrons convert to a proton, electron and antineutrino.
$Q=\left(m_n-m_p-m{_v}^--m_e\right) c^2=0.782 \mathrm{MeV}$

Atomic mass $(u)$ of Calcium is $40 u.$

A nucleus is made up of two fundamental particles$-$neutrons and protons. If a nucleus has more number of neutrons than what is needed to have stability, then neutrons decay into protons and if there's an excess of protons, then they decay to form neutrons. Since a neutron has larger rest mass than a proton, the $Q-$value of its decay reaction is positive and a free neutron decays to a proton, while an isolated proton cannot decay to a neutron as the $Q-$value of its decay reaction is negative. Hence, it is physically not possible.

${ }_{86} \mathrm{Rn}^{220} \rightarrow{ }_{84} \mathrm{Po}^{216}+z \mathrm{X}^A$
$Z + 84 = 86$ and $220 = 216 + A$
So, $Z = 2$ and $A = 4$
$2​​\alpha^4$
So, it is $\alpha$ particle.

Lithium atom contains $3$ protons and $3$ neutrons in the nucleus and $3$ valence electrons. When two lithium nuclei are brought together, they repel each other. The attractive nuclear forces being short$-$range are insignificant as compared to the electrostatic repulsion. Thus, the nuclei do not combine to form carbon atom because of coulomb repulsion.

The average binding energy per nucleon is just the total binding energy divided by the number of nucleons. If we consider Na atom, its binding energy is $194\ MeV.$
Its binding energy per nucleon is given by $\frac{194\text{MeV​}}{24}$
$= 8.08\ MeV$

Key Concept:

Isotopes of an element must have same atomic number $(Z)$ but different mass number $A.$
Number of protons is equal to the atomic number.
So, isotopes of an element have same number of protons.
Mass number is equal to the sum of number of protons and neutrons i.e. $A = p + n$
As isotopes of an element have different mass number but same number of protons, thus they must have different number of neutrons.

$^{40}_{19}{\text{K}}$ is the radioactive isotope of Potassium element.
As it has more number of neutrons than number of protons.

When an alpha particle is emitted from the nucleus the nucleus losses two protons and two neutrons. This means that the atomic number is decreased by $2.$