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

False. Bq counts decays per second in the source; danger depends on the energy that reaches you ($D$ in Gy) and its biological weight ($H$ in Sv). A weak-Bq alpha emitter swallowed can harm more than a huge-Bq gamma source across the room. See Radioactive decay law.

False. Both have units J/kg, but Gy is pure physics (energy per mass, $D$) and Sv is Gy multiplied by the radiation weighting factor, $H=w_{R}D$. They coincide only when $w_R=1$ (gamma, beta, X-rays); for alpha $1\text{Gy}=20\text{Sv}$.

False. Attenuation is exponential, $I=I_0{e}^{-\mu x}$, not linear. With $n$ = number of HVLs, the surviving fraction is $(1/2{)}^n$ and the blocked fraction is $1-(1/2{)}^n$: going from $n=1$ to $n=2$ HVL takes survival from $1/2$ to $1/4$ (blocking $3/4$), not "twice as much". See Figure 1.

False. Decay is memoryless — a fixed probability $\lambda$ per second, independent of age. The nucleus doesn't wear out; that's exactly why activity follows the exponential Radioactive decay law.

True. Since $A=\lambda N$ and $\lambda =\ln 2/t_{1/2}$, a smaller $t_{1/2}$ gives a larger $\lambda$, hence more decays per second for the same $N$. See Half-life.

False. Lead is ideal for gamma/X-rays (high-Z, dense), but for neutrons you want hydrogen-rich material (water, paraffin) to slow them; lead barely moderates them. For beta, low-Z material avoids extra bremsstrahlung X-rays. See Types of radiation (alpha beta gamma).

False. Dose falls as the Inverse-square law: intensity $\propto 1/r^2$, so twice the distance gives one-quarter the dose, not half (see Figure 2).

False. $w_R=1$ is a reference baseline, not "zero harm". Gamma still deposits energy ($D$ in Gy) and causes biological damage ($H$ in Sv, equal to Gy here); it just isn't extra-damaging per joule the way alpha is. See Biological effects of radiation.

The error ignores ingestion/inhalation. Outside the body, alpha is stopped by skin; inside, there is no paper — its $w_R=20$ makes it the most damaging per joule. Location, not just penetration, matters.

Exponential attenuation $I=I_0{e}^{-\mu x}$ never reaches zero for any finite thickness $x$. You can make it arbitrarily small, but "fully stopped" is impossible for gamma — only reducible.

24 mm is two HVLs ($n=2$ half-value layers), which leaves $(1/2{)}^2=1/4$ of the beam — it blocks three-quarters, not all. Confusing "two half-value layers" with "complete stopping".

Bq is decays per second, so $\lambda$ must be in ${\text{s}}^{-1}$. Mixing years with a per-second unit gives an answer wrong by a factor of ~$3\times 10^7$. Always match time units first.

No — as defined above, $w_T$ are tissue weighting factors (organ sensitivity, summing to 1), and $H_T$ is that organ's equivalent dose. The radiation-type weighting is $w_R$, applied earlier inside $H=w_{R}D$. Two different weightings ($w_T$ = organ, $w_R$ = radiation) for two different questions.

The Ci is just a larger unit, like a kilometre vs a metre. A source of $1\text{Bq}$ and a source of $2.7\times 10^{-11}\text{Ci}$ are identical activity — the number, not the unit name, sets the amount.

Bond-breaking chemistry depends on energy shared among the atoms present, and equal volumes of different density hold different amounts of matter. Dividing by mass gives "energy per kilogram of stuff", which is what tissue damage tracks. See Nuclear binding energy for why the energies are so large.

Both share the logic "constant probability per step": each thin slab has a fixed chance $\mu dx$ of removing a photon, just as each nucleus has a fixed chance $\lambda dt$ of decaying. Same differential equation $\Rightarrow$ same $e^{-(\text{rate})(\text{variable})}$ form.

When alpha does reach tissue (e.g. inhaled), it dumps its energy in an extremely short, dense track, ionizing many atoms close together and shredding DNA beyond repair. It's the density of ionization, not the range, that sets biological severity. See Biological effects of radiation.

Fast electrons decelerating in high-Z material emit penetrating bremsstrahlung X-rays — you'd trade one hazard for another. Low-Z material stops beta with far less secondary radiation. See Types of radiation (alpha beta gamma).

Because intensity from a point source obeys the Inverse-square law ($I\propto 1/r^2$) — simply stepping back is a free, powerful dose reduction requiring no material at all. It is the D of T-D-S.

Equivalent dose accumulates: even a small decay rate, integrated over long exposure Time (the T of T-D-S), and weighted by $w_R$, can sum to a significant Sv. Bq is a rate, Sv is a total.

$\lambda =0$, so $A=\lambda N=0$ — no decays. Then $t_{1/2}=\ln 2/\lambda \to \infty$: a stable isotope has an infinite half-life, consistent with never decaying.

$e^0=1$, so $I=I_0$ — the beam before the shield is unchanged, no attenuation. The formula correctly reproduces the "no barrier" limit as a sanity check.

They are numerically identical: $H=1\cdot D$, so 0.3 Gy of gamma = 0.3 Sv. This coincidence is why people mistakenly treat Gy and Sv as the same unit in general.

$I=I_0{e}^{-\mu x}\to 0$ but never equals zero — the asymptote is the mathematical statement that gamma is only ever attenuated, never perfectly stopped.

After $n$ half-lives $A=A_0(1/2{)}^n$, shrinking geometrically. It approaches zero but never reaches it in the continuous model — the source becomes negligible, not truly extinct. See Half-life.

Not directly — $1/r^2$ assumes a point source spreading over a sphere of area $4\pi r^2$. An infinite plane source gives nearly constant intensity with distance, so the "step back" trick is far weaker. The geometry of spreading is what the Inverse-square law encodes.