Nuclear structure — protons, neutrons, nuclear forces

2.3.18 · Physics › Modern Physics

1. Nucleus kis cheez se bana hai?

Yeh numbers ka matlab kya hai?

Atomic number $Z$ = protons ki sankhya → element fix karta hai.
Mass number $A$ = nucleons ki sankhya = $Z + N$ , jahan $N$ = neutrons ki sankhya.
Notation: $_{Z}^{A} X$ , jaise $_{6}^{12} C$ mein 6 protons, 6 neutrons hain.

2. Nucleus kitna bada hota hai? (Radius law derive karna)

$R = R_{0} A^{1/3}$ scratch se derive kaise karein:

Nucleus ka volume (sphere): $V = \frac{4}{3} π R^{3}$ .

Har nucleon ek fixed volume $v_{0}$ occupy karta hai, aur $A$ nucleons hain, isliye $V = A v_{0} .$

Dono ko equal set karo: $\frac{4}{3} π R^{3} = A v_{0} \Rightarrow R^{3} = \frac{3 v _{0}}{4 π} A \Rightarrow R = R_{0} (\frac{3 v _{0}}{4 π})^{1/3} A^{1/3} .$

3. Nuclear (strong) force — protons kyun alag nahi udte

Figure — Nuclear structure — protons, neutrons, nuclear forces

4. Neutrons kyun zaruri hain (neutron ka role)

5. Mass defect & binding energy (numbers mein "yeh kyun tikta hai")

Recall Feynman: ek 12-saal ke bacche ko samjhao

Socho ek bag mein chhote magnetic marbles hain. Kuch marbles (protons) par "+" sticker laga hai aur woh push karte hain ek doosre ko. Lekin har marble par super-strong velcro laga hai jo sirf usse touching marbles ko pakadta hai. Velcro push karne se bahut zyada strong hai, isliye bag ek saath clumped rehta hai. Hum kuch sticker-less marbles (neutrons) add karte hain — woh extra velcro laate hain lekin koi pushing nahi, isliye woh clump ko saath hold karne mein madad karte hain. Velcro tab hi kaam karta hai jab marbles touch karein (super short range); door se sirf pushing feel hoti hai.

Mass number

A

aur atomic number

Z

define karo.

Z

= protons ki sankhya (element fix karta hai);

A

= total nucleons =

Z + N

Isotopes kya hote hain?

Same

Z

lekin different

A

wale nuclei (same element, different neutron count).

Nuclear radius formula derive aur state karo.

Constant density se,

V \propto A

toh

R \propto A^{1/3}

;

R = R_{0} A^{1/3}

R_{0} \approx 1.2

fm.

Kya sabhi nuclei ki nuclear density same hoti hai? Kyun?

Haan (~

2.3 \times 1 0^{17}

kg/m³); mass ∝

A

aur volume ∝

A

cancel ho jaate hain.

Nuclear force ki 4 properties list karo.

Strongest, short-ranged (~2–3 fm), charge-independent, saturated (sirf nearest neighbours); repulsive core <0.5 fm.

Nuclear force short-ranged kyun hai (Yukawa)?

Yeh ek massive particle (pion) se mediate hoti hai; range

\sim ℏ/ (m_{π} c) \approx 1.4

fm. Massive mediator → finite range.

Saturation kyun imply karta hai ki

E_{B} \propto A

hai,

A^{2}

nahi?

Har nucleon sirf fixed nearest neighbours se bond karta hai, isliye total bonds

A

ke saath scale karte hain, na ki sabhi pairs ke saath.

Heavy nuclei ko extra neutrons (

N > Z

) kyun chahiye?

Neutrons strong attraction add karte hain bina Coulomb repulsion ke,

Z^{2}

-growing proton repulsion ko balance karte hue.

Mass defect aur binding energy define karo.

Δ m = [Z m_{p} + N m_{n}] - M_{n u c l e u s}

;

E_{B} = Δ m c^{2}

Conversion:

1

u·

c^{2}

= ?

931.5

MeV.

Bound nucleus apne parts se heavier hota hai ya lighter?

Lighter,

Δ m

se; khoyi hui mass binding energy ban jaati hai.

Connections

Mass defect and binding energy curve
Einstein mass-energy equivalence E=mc^2
Coulomb's law and electrostatic repulsion
Heisenberg uncertainty principle (Yukawa range estimate)
Radioactive decay — alpha, beta, gamma
Nuclear fission and fusion
Rutherford scattering experiment

Nuclear structure — protons, neutrons, nuclear forces

1. Nucleus kis cheez se bana hai?

2. Nucleus kitna bada hota hai? (Radius law derive karna)

3. Nuclear (strong) force — protons kyun alag nahi udte

4. Neutrons kyun zaruri hain (neutron ka role)

5. Mass defect & binding energy (numbers mein "yeh kyun tikta hai")

6. Common mistakes (Steel-man + fix)

7. Forecast-then-Verify

Flashcards

Connections

Concept Map