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

1. Activity — the becquerel (Bq)

Derivation from scratch. Let $N$ = number of radioactive nuclei. The decay rate is proportional to $N$ : $-\frac{dN}{dt} = \lambda N \quad\Rightarrow\quad A \equiv -\frac{dN}{dt} = \lambda N$ Solving the ODE: separate variables $\frac{dN}{N} = -\lambda\,dt$ , integrate $\Rightarrow \ln N = -\lambda t + C$ , so $N = N_0 e^{-\lambda t}, \qquad A = A_0 e^{-\lambda t}.$ Why this step? Because $A=\lambda N$ and $N$ decays exponentially, activity decays with the same exponential.

The half-life $t_{1/2}$ comes from setting $N = N_0/2$ : $\tfrac12 = e^{-\lambda t_{1/2}} \Rightarrow \boxed{t_{1/2} = \frac{\ln 2}{\lambda}}$

2. Absorbed dose — the gray (Gy)

$D = \frac{E_{\text{absorbed}}}{m}$

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

Radiation	$w_R$
X-rays, $\gamma$ , $\beta$	1
protons	~2
$\alpha$ particles	20
neutrons	5–20 (energy dependent)

4. Shielding — exponential attenuation

Derivation. Let $I$ = beam intensity, $x$ = depth. Loss in a thin slab $dx$ is proportional to $I$ and $dx$ : $-dI = \mu I\,dx \Rightarrow \frac{dI}{I} = -\mu\,dx \Rightarrow \boxed{I = I_0 e^{-\mu x}}$ where $\mu$ = linear attenuation coefficient (units m⁻¹). Why this step? identical math to activity; the "constant chance per unit thickness" is the physical reason.

The half-value layer (HVL) — thickness halving intensity: $x_{1/2} = \frac{\ln 2}{\mu}$

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

Worked examples

Recall Feynman: explain to a 12-year-old

Imagine a popcorn machine. Bq = how many kernels are popping each second (the source). Gy = how much heat your hand soaks up if you hold it over the pot. Sv = how much that actually hurts — a tiny sharp pin (alpha) hurts way more than the same warmth from a soft glow (gamma), even if the energy is equal. Shielding = holding a lid: each lid blocks half, so two lids block three-quarters, three lids block seven-eighths — never quite all of it.

Flashcards

What does 1 Bq equal?

1 nuclear disintegration per second.

Convert 1 curie (Ci) to Bq.

1\ \text{Ci} = 3.7\times10^{10}\ \text{Bq}

Define the gray (Gy).

Absorbed dose = 1 joule of energy deposited per kilogram of matter (1 J/kg).

Define the sievert (Sv).

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

H=w_R D

); biological-harm unit.

Why are Gy and Sv numerically equal for gamma/beta?

Because their radiation weighting factor

w_R = 1

What is

w_R

for alpha particles, and so 0.5 Gy of α equals how many Sv?

w_R=20

; gives

0.5\times20 = 10

Sv.

What is the

w_R

range for neutrons?

About 5 to 20, depending on neutron energy.

State the activity formula and derive half-life.

A=\lambda N

; setting

N=N_0/2

N=N_0e^{-\lambda t}

gives

t_{1/2}=\ln 2/\lambda

Write the shielding attenuation law and define each symbol.

I=I_0 e^{-\mu x}

;

\mu

= linear attenuation coefficient,

x

= thickness.

What is the half-value layer (HVL) formula?

x_{1/2}=\ln 2/\mu

(thickness that halves intensity).

How many HVLs reduce intensity to 1/8?

3 HVLs, since

(1/2)^3=1/8

Best shielding for alpha, beta, gamma, neutrons?

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

Name the three pillars of radiation protection.

Time, Distance (inverse-square), Shielding.

Why divide absorbed energy by mass for dose?

Damage depends on energy per kg of tissue (bond-breaking density), not total energy or volume.

Connections

Radioactive decay law — same $e^{-\lambda t}$ math underpins both activity and shielding.
Half-life — $t_{1/2}=\ln2/\lambda$ reused as HVL.
Types of radiation (alpha beta gamma) — sets $w_R$ and shielding needs.
Inverse-square law — the "Distance" pillar.
Biological effects of radiation — why Sv exists.
Nuclear binding energy — source of the decay energy that becomes dose.

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, radiation safety mein teen alag sawaal hote hain, isliye teen alag units hain. Pehla — source kitni tezi se decay kar raha hai? Iska answer Becquerel (Bq) deta hai: 1 Bq matlab har second mein 1 nucleus toot raha hai. Ye purely source ki property hai, tumse koi lena-dena nahi. Activity formula $A=\lambda N$ hai, aur ye bhi $e^{-\lambda t}$ ke hisaab se ghatta hai, bilkul decay law jaise.

Dusra sawaal — tumhare tissue ne kitni energy soak ki? Iska unit Gray (Gy) hai, matlab joule per kilogram. Yahaan mass se divide karte hain kyunki damage "per kg tissue mein kitni energy ghusi" pe depend karta hai. Teesra aur sabse important — wo energy actually kitna nuksaan karegi? Iske liye Sievert (Sv) hai. Same Gy ki alpha radiation, gamma se 20 guna zyada khatarnaak hai, isliye $w_R$ (weighting factor) se multiply karte hain: $H=w_R D$ . Gamma/beta ke liye $w_R=1$ to Gy aur Sv numerically same dikhte hain — yahin students confuse ho jaate hain. Yaad rakho: Gy = physics (energy), Sv = biology (harm).

Shielding ka jaadu bhi exponential hai: $I=I_0 e^{-\mu x}$ . Har patli layer fixed fraction rokti hai, isliye intensity exponentially girti hai. Half-value layer (HVL) wo thickness hai jo intensity aadhi kar de. Do HVL se 1/4, teen se 1/8 — kabhi poora zero nahi hota gamma ke liye. Practical rule yaad karo: alpha ko paper/skin rok deta hai, beta ko thin aluminium, gamma ko mota lead/concrete, aur neutron ko paani ya paraffin (hydrogen-rich). Aur teen golden rules: Time kam, Distance zyada (inverse-square), aur Shielding — bas yahi 80% radiation safety hai.

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

1. Activity — the becquerel (Bq)

2. Absorbed dose — the gray (Gy)

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

4. Shielding — exponential attenuation

Worked examples

Flashcards

Connections

Concept Map

Hinglish (regional understanding)

Go deeper — visual, from zero

Test yourself — Nuclear & Radiochemistry

Connections