Question

The heat production (\(Q_r\)) of a granitic rock due to decay of the radioactive elements U, Th and K having concentration \(C_U, C_{Th}, C_K\), respectively, is given by the expression: \[ Q_r = \alpha C_U + \beta C_{Th} + \gamma C_K \] Which one of the following correctly represents the relation between the magnitude of coefficients \(\alpha, \beta, \gamma\) (in \(\mu Wkg^{-1}\))?

• A. \(\alpha > \beta > \gamma\)
• B. \(\alpha < \beta > \gamma\)
• C. \(\alpha > \beta < \gamma\)
• D. \(\alpha < \beta < \gamma\)

Hint:

In radioactive heat generation problems: Uranium contributes most, Thorium next, and Potassium least. Always remember the order: \(U > Th > K\).

Answer 1

The Correct Option is A

Step 1: Recall radioactive heat production. Different radioactive isotopes release heat at different rates depending on their decay constant and energy released per decay. The three main contributors in granitic rocks are: - Uranium (U), - Thorium (Th), - Potassium (K).

Step 2: Relative contributions. - Uranium produces the largest heat per unit mass because of its relatively short half-life and high energy release. - Thorium produces less heat compared to Uranium, but still significant. - Potassium (\(^{40}K\)) contributes the least per unit concentration because of its long half-life and low abundance.

Step 3: Order of coefficients. Thus, the heat production constants follow: \[ \alpha \, (\text{for U}) > \beta \, (\text{for Th}) > \gamma \, (\text{for K}) \]

Final Answer: \[ \boxed{\alpha > \beta > \gamma} \]