Physics M.C.Q (1 Marks)

The nuclear reaction: ${ }_{15} \mathrm{P}^{30} \rightarrow{ }_4 \mathrm{Si}^{30}+{ }_{+1} \mathrm{e}^0$
Thus a positron is emitted during the decay of ${ }_{15} \mathrm{P}^{30}$ into ${ }_{14} \mathrm{Si}^{30}$

The maximum binding energy per nucleon occurs at around mass number $A = 50$, and corresponds to the most stable nuclei. Iron nucleus $F^{56}$ is located close to the peak with a binding energy per nucleon value of approximately $8.8\ MeV$ . It’s one of the most stable nuclides that exist.

Fusion reactions takes place at temperature about $10^7\ K$ it requires this high temperature so that nucleus are moving at very high speed, so that they have high kinetic energy and can overcome the repulsion between nuclei and come together.

$^{22}$Ne decays
$\alpha$ particle $= He^{2+}$
Mass No $= 4$
$p = 2, n = 2$
So, New mass no. $= 22 − 8 = 14$
Atomic No. $= 10 − 4 = 6$
So, the new element is ${6^C}^{14}$

Binding energy per nucleon increases with atomic number. The greater the binding energy per nucleon the more stable is the nucleus.
For $_{26} \mathrm{Fe}^{56}$number of nucleons is $56.$
This is most stable nucleus, since maximum energy is needed to pull a nucleon away from it.

Fusion reaction takes place at temperatures around $10^7k$. It requires this high temperature so that nucleus start moving at rapidly speed, which in turn increases their kinetic, so that they overcome the repulsion between them and can come together.

Hydrogen has $3$ isotopes namely. protium $1​\text{H}\\1$, deuterium $2\text{H}\\1$ and tritium $3\text{H}\\1$

$^{57}Co$ is undergoing beta decay, i.e. electron is being produced. But an electron has very less mass $(9.11 \times 10^{-31}kg)$ as compared to the $Co$ atom. Therefore, after $570$ days, even though the atoms undergo large beta decay, the weight of the material in the container will be nearly $10g.$

The half$-$life of a radioactive sample $\Big(\text{t}_{\frac{1}2{}}\Big)$ is defined as the time elapsed before half the active nuclei decays.
Let the initial number of the active nuclei present in the sample be $N_0$.
$\frac{\text{N}_{0}}{2}=\text{N}_{\text{0}}\text{e}^{-\lambda\text{t}_{\frac{1}2{}}}$
$\Rightarrow\text{t}_{\frac{1}{2}}=\frac{\text{In}2}{\lambda}$
Average life of the nuclei, $\text{t}_{\text{av}}=\frac{\text{S}}{\text{N}_{0}}=\frac{1}{\lambda}$
Here, $S$ is the sum of all the lives of all the $N$ nuclei that were active at $t = 0$ and $\lambda$ is the decay constant of the sample.

$\beta^-$ emission is due to decay of neutron in the nucleus $n \rightarrow p + e^-$.

From conservation of energy:
Change in energy $=$ Energy of reactants $−$ Energy of products $− Q>0 ($Endothermic$)$
Therefore, minimum energy of reactants $>Q=11.32\ MeV$

In nuclear physics, a unit used for measurement of mass is unified atomic mass unit, which is denoted by $u.$
It is defined such that
$1\text{u}=\frac{1}{12}\times ($Mass of neutral carbon atom in its ground state$)$
Mass of neutral carbon atom in its ground state $= 12 \times 1u = 12u$
Thus, the mass of neutral carbon atom in its ground state is exactly $12u.$

Nuclear fusion is a reaction in which two or more atomic nuclei come close enough to form one or more different atomic nuclei and subatomic particles $($neutrons and/or protons$).$
The difference in mass between the products and reactants is manifested as the release of large amounts of energy.
A hydrogen bomb derives its energy from this type of nuclear reaction.

Binding energy per nucleon $= 5.6MeV$
No. of nucleon $=$ No. of proton $+$ No. of neutron
$= 3 + 4 = 7$
So, for $7$ Nucleon $= 7 \times 5.6 = 39.2\ MeV$

1. Fusion requires temperatures about $100$ million Kelvin $($approximately six times hotter titan the sun’s core$).$
2. At these temperatures, hydrogen is a plasma, not a gas. Plasma is a high$-$energy state of matter in which all the electrons are stripped from atoms and move freely about.
3. The sun achieves these temperatures by its large mass and the force of gravity compressing this mass in the core. We must use energy from microwaves, lasers and ion particles to achieve these temperatures.

1. The sun uses its mass and the force of gravity to squeeze hydrogen atoms together in its core.
2. We must squeeze hydrogen atoms together by using intense magnetic fields, powerful lasers or ion beams.

Radiocarbon is produced in the atmosphere as result of collision between fast neutrons and nitrogen nuclei present in the atmosphere.
Nuclear reaction is given as:
${ }_7 \mathrm{~N}^{14}+{ }_0 \mathrm{n}^1 \rightarrow{ }_6 \mathrm{C}^{14}+{ }_1 \mathrm{H}^1$

In a Bainbridge mass spectrometer positive rays of the same element produce different traces. The traces correspond to isotopes. Isotopes are atoms of same element. They have same atomic number $($nuclear charge$)$ but different mass number $($number of neutrons$)$. Positive rays $($or anode rays or canal rays$)$ contains ions obtained by knocking out electrons from gaseous atoms.

$\left(\mathrm{NH}_4\right)_2 \mathrm{CO}_3$​ is the chemical formula of ammonium carbonate.
$N = 14 \times (2) = 28$
$H = 1 \times (4\times 2) = 8$
$C = 12 \times 1 = 12$
$O = 16 \times 3 = 48$
Molar mass $= 28 + 8 + 12 + 48 = 96\ g/mol$

Magnetic force acts on a charged particle, due to which it deflects from its path. The magnitude of this force is measured as $\Big|\overrightarrow{\text{F}}\Big|=\Big|\text{q}\Big(\overrightarrow{\text{v}}\times\overrightarrow{\text{B}}\Big)\Big|.$
Here, $q$ is the charge on the particle that is moving with speed v in a uniform magnetic field $B$.
Since alpha, beta$-$plus and beta$-$minus are charged particles, they suffer deflection due to the field applied. On the other hand, gamma rays are photons and due to zero charge, they do not suffer any deflection.

After release of helium, there will be decrease in atomic number by $2$ and mass number by $4.$

Cobalt therapy or cobalt $-60$ therapy is the medical use of gamma rays from the radioisotope cobalt $60$ to treat conditions such as cancer.

Alpha particle has highest mass of the given option which is he rest mass of the alpha particle amounts to $6.64424 \times 10^{-27} \mathrm{~kg}$. Mass of neutron is $1.0086654 a.m.u.$
Mass of electrons $=9.10938291 \times 10^{-31}$ kilograms.
Hence mass of alpha particle is greatest.