Question

Arrange the following materials in ascending order of their probabilities of photo-electric effect for a $100 \text{ keV}$ photon.
A. C
B. O
C. Sn
D. Pb
E. Ca

• A. \(D < C < E < B < A \)
• B. \(A < B < E < C < D \)
• C. \(A < B < C < D < E \)
• D. \(D < E < B < C < A \)

Hint:

Lead (Pb) is used in shielding because its high atomic number ($Z=82$) makes it extremely effective at absorbing high-energy photons via the photoelectric effect.

Answer 1

The Correct Option is B

Concept: The probability of the photoelectric effect (cross-section $\sigma$) for high-energy photons (X-raysGamma rays) is strongly dependent on the atomic number ($Z$) of the material. The relation is approximately: \[ \sigma \propto \frac{Z^n}{E^3} \] where $n$ is typically between 4 and 5. This means as the atomic number increases, the probability of the photoelectric effect increases significantly.

Step 1: Identify the atomic numbers ($Z$) of the given elements.

• A. Carbon (C): $Z = 6$
• B. Oxygen (O): $Z = 8$
• E. Calcium (Ca): $Z = 20$
• C. Tin (Sn): $Z = 50$
• D. Lead (Pb): $Z = 82$

Step 2: Arrange in ascending order of probability.
Since $\sigma \propto Z^n$, the ascending order of probability follows the ascending order of atomic numbers: Order: Carbon < Oxygen < Calcium < Tin < Lead. This corresponds to: \(A < B < E < C < D\).