Question

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?

Answer 1

Answer:

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