The correct answer is - Magma generated from a hot spot burned through the overlying plate to create volcanoes.
The Hawaiian Islands are all formed as a result of volcanic activity of a hot spot. The hot spot is stationary, but the islands are in the shape of a chain, not all in the same place. Also, the rocks on the islands that do not have active volcanoes are older, than the ones that do have volcanic activity. This suggests that the Pacific plate is moving. According the direction in which the islands are arranged, the Pacific plate seems to move toward northwest. As it moves, it moves over the hot spot. Since the hot spot is stationary, as the Pacific plate moves, eventually the volcanic activity will stop on the island that has moved further away from the hot spot. The magma from the hot spot will penetrate through the crust that came to be over it. That will result in new volcanic island emerging from the sea over the hot spot. The process goes on for millions of years, and it can result in hundreds of islands of volcanic origin.
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Answer:
The age of the rock = 2800.6 million years = 2.8 billion years.
A simple method of analysis similar to Carbon dating is used to obtain the required age of the rock. Radioactive substances decay according to first order reaction kinetics. So, plugging all the required parameters into the general equation for amount of substance left in a first order decay gives us the age of the rock.
Explanation:
Half life of Uranium-235 = 700 million years (from literature)
The decay of radioactive substances follow first order reaction kinetics.
The general equation is given as
A(t) = A₀ e⁻ᵏᵗ
A(t) = Amount of radioactive substance left after a particular time = 6.25%
A₀ = initial amount of radioactive substance = 100%
t = time that has passed since the beginning = age of the rock = ?
k = decay constant
The decay constant is related to the half life (T) through the relation,
k = (In 2)/T
k = (0.693/700) = 0.00099 /million years
A(t) = A₀ e⁻ᵏᵗ
6.25 = 100 e⁻ᵏᵗ
0.0625 = e⁻ᵏᵗ
In e⁻ᵏᵗ = In 0.0625 = -2.7726
-kt = - 2.7726
t = (2.7726/0.00099) = 2800.6 million years
t = 2.8 billion years.
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