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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