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GATE-2023 (17)

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17. The heat production (Q_r) of a granitic rock due to the decay of the radioactive elements U, Th, and K having concentrations Cu, CTh, and CK, 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 a, b, g (in mWkg^−1)?

A)\alpha >\beta >\gamma

B)\alpha < \beta> \gamma

C)\alpha > \beta < \gamma

D)\alpha < \beta < \gamma

Solution:

The amount of heat generated per second by these elements (in mWkg^−1 ) are: natural uranium, 95.2; thorium, 25.6, and natural potassium 0.00348 (Rybach, 1976; 1988).

The heat Q_r produced by radioactivity in a rock that has concentrations C_u, C_{Th}, C_K, respectively, of these elements is

Q_r=95.2 C_u+ 25.6 C_{Th} +0.00348 C_K ---(1)

Based on the above equation \alpha >\beta >\gamma

Concentration (p.p.m by weight) of granite C_U=4.6, C_{Th}=18, and C_K=33,000

Substitute these values in the above equation (1)  

Q_r=437.92+ 460.8 +114.84

Q_r=1013.56 ---(2)


The answer is option (A)


References: 

1. Fundamentals of Geophysics by William Lowrie.

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