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Uranium -238 has a half-life of 4.5 billion years. When the Earth was formed, there was twice as much uranium -238 present as there is now. What is the age of the Earth?

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ZekeVeteran · Tutor for 12 years

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The age of the Earth is 4.5 billion years.

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## Step 1: We know that the half-life of an element is the amount of time for the original mass to diminish by 50%. ## Step 2: Given that Uranium-238 has a half-life of 4.5 billion years, this means if we started with a certain amount of Uranium-238, after 4.5 billion years, only 50% of that amount will remain, the rest will have decayed. ## Step 3: We are told that "When the Earth was formed, there was twice as much uranium-238 as there is now." This implies that Earth has experienced exactly one half-life, since half of the original amount of Uranium-238 when Earth formed has decayed and half remains. ### Therefore by following the principle of half-life of uranium \[ \text{{Age of Earth}} = \text{{half-life of uranium}} = 4.5 \text{{ billion years}} \]

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Uranium -238 has a half-life of 4.5 billion years. When the Earth was formed, there was twice as much uranium -238 present as there is now. What is the age of the Earth?

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