Question

1. Calculate the rate of heat production per unit mass (W/kg) by radiogenic elements in the following rock samples. Assume

that uranium has a heat production rate of 9.81x10^-5 W/kg, thorium has a heat production rate of 2.64x10^-5 W/kg, and

potassium has a heat production rate of 3.48x10^-9 W/kg. Concentrations are given in kg/kg

a)A sample of continental crust with radiogenic concentrations listed below: U 1.42 parts per million, Th 5.60 parts per million, and K 1.43 parts per hundred

b)A sample of mantle-derived peridotite with radiogenic concentration listed blow: U 1 parts per billion, Th 4 parts per billion, and K 30 parts per million

c)A sample of chondritic meteorite with radiogenic concentrations listed below:U 8 parts per billion, Th 29 parts per billion, K 560 parts per million

2.

From the concentrations listed above, what can you say about the partitioning (ie. dividing up) of radiogenic elements between the crust and mantle, and what are the implications for internal heat production in the earth today? Note that chondritic meteorites are considered to have concentrations similar to the primordial earth.

Answer 1

1)Here we have given that,

The rate of heat production of Uranium(U)

Rate of heat production of Thorium(Th)

Rate of heat production of Pottassium(K)

a) for the sample of continental crust,

Concentration are given in (Kg/Kg)

Radiogenic concentration of Uranium(U)=1.42 ppm

Which indicates that for a rock of 1million Kg,1.42Kg of uranium are present.

So heat produced by Uranium

Radiogenic concentration of Thorium(Th)=5.6 ppm

Ie, 5.6Kg Thorium present in 1 million Kg of rock

Heat produced by the Thorium(Th),

Radiogenic concentartion of Pottassium(K)=1.43Parts per hundred=14300ppm

Ie,14300Kg of pottassium in 1million Kg of rock.

Heat produced by Pottassium,

So,for 1 million of Rock of continental crust,total heat produced by all the radiogenic elements(U,Th and K)

or,

Here the total power of radiogenic heat produced from the 1millon of the continental crust rock

So,Rate of heat produced per unit mass of rock,

b) Radiogenic concentration of mantle derived periodite rock for each elements are,

Radiogenic concentration of Uranium(U)=1parts per billion=0.001ppm

So, for 1 million kg of rock 0.001kg of uranium present.

Heat produced by Uranium,

Radiogenic concentration of Thorium(Th)=4parts per billion=0.004ppm

So,0.004 kg of Thorium in 1million Kg of rock.

Heat produced by Thorium,

Radiogenic concentration of Pottassium,K=30ppm

Ie,30kg of pottassium in 1million Kg of rock.

So,heat produced by Pottassium,

total heat produced,

So,Total Radiogenic power produced by 1 million Kg of Mantle derived periodite rock,

So,Rate of heat produced per unit mass of rock,

c) Radiogenic concentration of chonditic mateorite rock for each elements are,

Radiogenic concentration of Uranium(U)=8parts per billion=0.008ppm

So, for 1 million kg of rock 0.008kg of uranium present.

Heat produced by Uranium,

Radiogenic concentration of Thorium(Th)=29parts per billion=0.029ppm

So,0.029 kg of Thorium in 1million Kg of rock.

Heat produced by Thorium,

Radiogenic concentration of Pottassium,K=560ppm

Ie,560kg of pottassium in 1million Kg of rock.

So,heat produced by Pottassium,

So,Total Radiogenic power produced by 1 million Kg of Chondritic meteorite rock,

So

So,Rate of heat produced per unit mass of rock,