Question

3. About how many carbon-14 atoms from a sample of 800C-14 atoms will remain after 2.0 half-lives? (Show your work)

4. About how many N-14 atoms will be present from a sampleof 800 C-14 atoms after 2.0 half-lives? (Show your work)

5. 100 C-14 atoms remain from a sample of 1600 C-14 atoms.
a. How many half-lives have passed? (Show your work)
b. How much time has passed? (The half life of C-14 is5730 years) (Show your work)

Answer 1

Concept:

Radioactivity is a spontaneous phenomenon of the disintegration of unstable atomic nuclei into more energetically stable atomic nuclei.

Radioactive decay law,

N=N₀e^(-λt)

The rate of change in the number of particles is known as Activity.

Given:

The initial number of the carbon atoms, and half-lives.

Find:

The remaining sample of Carbon-14 atoms.

Solution:

3. Remained amount can be calculated by the formula,

N/N₀=(1/2)ⁿ

Where N is the remained amount, N₀ is the initial amount and n is the number of half-lives.

Given, that the initial amount of radioactive substance = 800 atoms

After 2 half-lives,

Amount remained, N = (1/2)² x 800 = 200 atoms

Hence, the total of 200 atoms of the carbon-14 atoms from a sample of 800C-14 atoms will remain after 2.0 half-lives.

4. The number of the N-14 atoms will present in a sample of 800 C-14 atoms after 2.0 half-lives will be the same as that of the number of atoms present in C-14 atoms because the carbon-14 is radioactive and very unstable, So, they transform them into Nitrogen to gain stability.

5.  (a) The number of half-lives can be calculated by the formula,

N/N₀=(1/2)ⁿ

Where N is the remained amount, N₀ is the initial amount and n is the number of half-lives.

Given, that the initial amount of radioactive substance = 1600 atoms and remained amount = 100 atoms

Number of half-lives,

100/1600  = (1/2)ⁿ

Comparing, n = 4

Hence, to remain 100 C-14 atoms from a sample of 1600 C-14 atoms, 4 half-lives are passed

(b) As the 4 half-lives are passed, and one half-life of C-14 is 5730 years.

So, t = 4 × 5730 = 22920 years.

As the 4 half-lives are passed, a total of 22920 years is passed to remain 100 C-14 atoms from a sample of 1600 C-14 atoms.

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