A granite contains zircon crystals with 275 billion 235U atoms and 1925 billion 207Pb atoms. The half-life for 235U-to-207Pb decay is 704 million years. How old is the granite?

The granite that contains zircon crystals with 275 billion 235U atoms and 1925 billion 207Pb atoms is 2112 million years old.

From the given information:

the total number of parent atoms is equal to the total number of ²³⁵U atoms

Now, from these 2200 billion atoms, 1925 billion of ²³⁵U atoms has changed to Pb²⁰⁷ atoms.

So when the number of half-life is:               the parent atom is:

0                                                                      2200 billion

1                                                                        1100 billion

2                                                                       550 billion

3                                                                       275 billion

It implies that the parent atoms have passed through three half-life;

Thus, the age of the granite(parent atom) is calculated as:

age of granite = n ×

age of granite  = 3 × 704 million years

age of granite  = 2112 million years

Therefore, the age of granite is 2112 million years.

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The correct answer would be = t = 2.112 billion years

Explanation:

Given:

The number of crystal of uranium = 275 billion

The number of crystal of lead = 1925 billion

The half-life for 235U = 704 million years

Formula using :

N = N0e−λt

where,

no. of daughter atoms = N

at time t= 0, No. of parent atoms = N0.

Time  = T

Half life = 0.693/λ

Decay constant = λ

Solution:

by putting value in the formula of the half-life

λ = 0.693/0.704

λ = 0.9844

Now, putting value in the formula for the age of granite.

275 = (275+1925)e^-0.9844 t

1/8= e^-0.9844 t

e^0.9844 t = 8

taking log

0.9844t = 2.07944

t = 2.112 billion years