Uranium-238 Decay and Half-Life

The video tutorial explains how to determine the fraction of uranium-238 remaining on Earth after 5 billion years, given the age of Earth and the half-life of uranium-238. It covers the calculation of the decay constant and the application of the decay formula to find the remaining fraction of uranium. The tutorial concludes that half of the original uranium-238 remains after 5 billion years.

What is the age of the Earth as mentioned in the problem?

• 5 into 10^9 years

• 5 million years

• 5 into 10^6 years

• 5 billion years

What is the half-life of Uranium-238 according to the video?

• 5 million years

• 5 billion years

• 10 million years

• 10 billion years

What does the age of the Earth represent in this problem?

• The time since the formation of the Earth

• The time since the last ice age

• The time since the first human appeared

• The time since the last volcanic eruption

How is the decay constant (K) calculated?

• By multiplying the half-life by 0.693

• By dividing 0.693 by the half-life

• By adding 0.693 to the half-life

• By subtracting 0.693 from the half-life

What is the value of the decay constant (K) calculated in the video?

• 5 into 10^9 per year

• 1.38 into 10^10 per year

• 0.693 per year

• 1.38 into 10^-10 per year

Which formula is used to find the fraction of Uranium-238 remaining?

• x0/X = T / K

• log(x0/X) = K * T / 2.3

• log(x0/X) = K / T

• x0/X = K * T

What is the purpose of finding the antilog in the calculation?

• To eliminate the logarithm and find the fraction

• To find the half-life

• To increase the value of X

• To decrease the value of X

What is the final fraction of Uranium-238 remaining after 5 billion years?

• 0.5

• 0.75

• 1.0

• 0.25

What does the final calculation of 1/1.99 represent?

• The decay constant

• The remaining fraction of Uranium-238

• The initial amount of Uranium-238

• The age of the Earth

What is the significance of the value 0.5 in the context of the problem?

• It represents the decay constant

• It is the fraction of Uranium-238 that has decayed

• It is the age of the Earth

• It is the fraction of Uranium-238 still present