Question

Numerical Geologic Time - Calculation A granite contains zircon crystals with 175 billion 235U atoms and 1225 billion 207Pb atoms. The half-life for 235U-to-207Pb decay is 704 million years. How old is the granite? Steps: Calculate the total number of parent and daughter atoms (equaling the original number of parent atoms when the rock formed). Figure out how many half-lives have gone by until the current number of parent atoms was reached (by repeatedly dividing the original number by 2). Multiply this number of half-lives by the years that correspond to one half-life.

Answer 1

Step-by-step explanation:

To calculate the age of the granite, you can follow these steps:

1. Calculate the number of half-lives that have occurred:

- Start with the number of 235U atoms (175 billion).

- Divide by 2 repeatedly until you get a number less than the number of 207Pb atoms (1225 billion). Count how many times you divided by 2.

2. Multiply the number of half-lives by the half-life of 235U-to-207Pb decay (704 million years).

Let's do the calculations:

Step 1:

- Start with 175 billion 235U atoms.

- After 1 half-life, you have 175 billion / 2 = 87.5 billion 235U atoms.

- After 2 half-lives, you have 87.5 billion / 2 = 43.75 billion 235U atoms.

- After 3 half-lives, you have 43.75 billion / 2 = 21.875 billion 235U atoms.

- After 4 half-lives, you have 21.875 billion / 2 = 10.9375 billion 235U atoms.

- After 5 half-lives, you have 10.9375 billion / 2 = 5.46875 billion 235U atoms.

So, it took 5 half-lives for the 235U atoms to decay to a number less than the number of 207Pb atoms.

Step 2:

- Now, multiply the number of half-lives by the half-life of 235U-to-207Pb decay:

5 half-lives x 704 million years/half-life = 3,520 million years.

So, the granite is approximately 3,520 million years old, which is equivalent to 3.52 billion years.