Question

Suppose the mantle of the Earth is 70% olivine, and that olivine on average has a dislocation density equal to what you just calculated (2.93*10^-4/nm^2). What is the total length of all dislocations in the mantle (if laid end to end) and how does that distance compare to distances or objects within the solar system, galaxy, or universe (as appropriate). Show your work and all parameters you use.

Answer 1

The earth's mantle is between core and crust and its a spherical hard shell of inner radius 3486 km and outer radius of 6320 km. (Data found from internet sources)

hence, the total volume of mantle is:

as 70% of this is olivine, hence

Dislocation density :

2.93 x 10^-4 /nm²

or

2.93 x 10^-4 / (10^-9 m)²

or

2.93 x 10^-4 / 10^-18 m²

2.93 x 10¹⁴ m²

For each cubic meter, length of dislocations is 2.93 x 10¹⁴ m,

Hence, for the total olivine volume inside the core the length of dislocations is:

L = 6.1593 x 10²⁰ x 2.93 x 10¹⁴ m = 18.046 x 10³⁴ m.

This is a huge length given that the size of solar system is of the order of 4.5 x 10¹² m, and the size of galaxy is of the order of 9.4 x 10²⁰ m, and size of universe is of the order of 4.35 x 10²⁶ m.

The Size of dislocation length is much more than universe.