Radiation safety — units (Bq, Gy, Sv), shielding

5.2.9 · Chemistry › Nuclear & Radiochemistry

1. Activity — the becquerel (Bq)

Derivation from scratch. Maano $N$ = radioactive nuclei ki sankhya. Decay rate $N$ ke proportional hai: $- \frac{d N}{d t} = λ N \Rightarrow A \equiv - \frac{d N}{d t} = λ N$ ODE solve karo: variables alag karo $\frac{d N}{N} = - λ d t$ , integrate karo $\Rightarrow ln N = - λ t + C$ , toh $N = N_{0} e^{- λ t}, A = A_{0} e^{- λ t} .$ Ye step kyun? Kyunki $A = λ N$ aur $N$ exponentially decay karta hai, activity bhi usi exponential se decay karti hai.

Half-life $t_{1/2}$ milti hai $N = N_{0} /2$ rakhne se: $\frac{1}{2} = e^{- λ t_{1/2}} \Rightarrow t_{1/2} = \frac{ln 2}{λ}$

2. Absorbed dose — the gray (Gy)

$D = \frac{E _{absorbed}}{m}$

3. Equivalent & effective dose — the sievert (Sv)

Radiation	$w_{R}$
X-rays, $γ$ , $β$	1
protons	~2
$α$ particles	20
neutrons	5–20 (energy dependent)

4. Shielding — exponential attenuation

Derivation. Maano $I$ = beam intensity, $x$ = depth. Ek thin slab $d x$ mein loss $I$ aur $d x$ ke proportional hai: $- d I = μ I d x \Rightarrow \frac{d I}{I} = - μ d x \Rightarrow I = I_{0} e^{- μx}$ jahan $μ$ = linear attenuation coefficient (units m⁻¹). Ye step kyun? Activity se identical math; "constant chance per unit thickness" physical reason hai.

Half-value layer (HVL) — woh thickness jo intensity aadhi kar de: $x_{1/2} = \frac{l n 2}{μ}$

Figure — Radiation safety — units (Bq, Gy, Sv), shielding

Worked examples

Recall Feynman: ek 12-saal ke bachche ko samjhao

Ek popcorn machine imagine karo. Bq = har second kitne kernels pop ho rahe hain (source). Gy = agar tum haath pot ke upar rakho toh kitni garmi sokhta hai tumhara haath. Sv = ye actually kitna dard karta hai — ek tiny sharp pin (alpha) kaafi zyada dard deti hai same energy ki soft glow (gamma) se, chahe energy barabar ho. Shielding = ek dhakkan pakadna: har dhakkan aadha rok leta hai, toh do dhakkan teen-chauthai rokte hain, teen dhakkan saat-aathwan — kabhi poora nahi rokta.

Flashcards

1 Bq kya hota hai?

1 nuclear disintegration per second.

1 curie (Ci) ko Bq mein convert karo.

1 Ci = 3.7 \times 1 0^{10} Bq

Gray (Gy) define karo.

Absorbed dose = matter ke 1 kilogram mein deposit ki gayi 1 joule energy (1 J/kg).

Sievert (Sv) define karo.

Equivalent/effective dose = absorbed dose weighted by radiation type (

H = w_{R} D

); biological-harm unit.

Gamma/beta ke liye Gy aur Sv numerically equal kyun hain?

Kyunki unka radiation weighting factor

w_{R} = 1

hai.

Alpha particles ke liye

w_{R}

kya hai, aur isliye 0.5 Gy of α kitne Sv ke barabar hai?

w_{R} = 20

;

0.5 \times 20 = 10

Sv milta hai.

Neutrons ke liye

w_{R}

range kya hai?

Lagbhag 5 se 20, neutron energy par depend karta hai.

Activity formula likho aur half-life derive karo.

A = λ N

;

N = N_{0} e^{- λ t}

mein

N = N_{0} /2

rakhne par

t_{1/2} = ln 2/ λ

milta hai.

Shielding attenuation law likho aur har symbol define karo.

I = I_{0} e^{- μx}

;

μ

= linear attenuation coefficient,

x

= thickness.

Half-value layer (HVL) formula kya hai?

x_{1/2} = ln 2/ μ

(woh thickness jo intensity aadhi kar de).

Intensity 1/8 karne ke liye kitne HVLs chahiye?

3 HVLs, kyunki

(1/2)^{3} = 1/8

Alpha, beta, gamma, neutrons ke liye best shielding?

α: paper/skin; β: thin Al/plastic; γ: high-Z lead/concrete; neutrons: hydrogen-rich (water/paraffin) + boron/cadmium.

Radiation protection ke teen pillars ke naam batao.

Time, Distance (inverse-square), Shielding.

Absorbed energy ko mass se kyun divide karte hain dose ke liye?

Damage energy per kg of tissue par depend karta hai (bond-breaking density), total energy ya volume par nahi.

Connections

Radioactive decay law — same $e^{- λ t}$ math activity aur shielding dono mein kaam karta hai.
Half-life — $t_{1/2} = ln 2/ λ$ HVL ke roop mein reuse hota hai.
Types of radiation (alpha beta gamma) — $w_{R}$ aur shielding needs set karta hai.
Inverse-square law — "Distance" pillar.
Biological effects of radiation — Sv kyun exist karta hai.
Nuclear binding energy — decay energy ka source jo dose ban jaati hai.