Radioactive uranium-235 has a half-life of about 700 million years. suppose you find a rock and chemical analysis tells you that only one sixteenth
of the rock's original uranium-235 remains. how old is the rock?

a.
2.8 billion years old

b.
1.4 billion years old

c.
175 million years old

d.
2.1 billion years old

e.
3.5 billion years old

f.
350 million years old

  A.  2.8 billion years old

Step-by-step explanation:

1/16 = (1/2)^4, so 4 half-lives have elapsed.

  4 · 0.700 billion years = 2.8 billion years

The rock is 2.8 billion years old.

Option A.

Step-by-step explanation:

Half life of Uranium-235 has been given as 700 million years.

Since radioactive decay is an exponential phenomenon so the formula will be

where = Amount of the radioactive element at the time 't'

= Initial amount

t = time for decay

k = decay constant

By this formula,

By taking natural log on both the sides,

0.693147 =

k =

  =

  =

Now we have to find the age of the rock which is one sixteenth of the original rock.

By the formula again,

Taking log on both the sides.

t =

t =

t =

Therefore, the rock is 2.8 billion years old.

Option A. is the answer.

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