Question

If there are 400 radioactive atoms in a sample, how many will remain after four half-lives have passed?
Enter the exact number as your answer. Do not spell out the number.

Answer 1

Answer:

25 atoms

Explanation:

Given data:

Total number of atoms = 400 atom

Atoms remain after 4 half lives passed = ?

Solution:

At time zero = 400 atom

At first half life = 400 atom/2 = 200 atom

At 2nd half life = 200 atom/2 = 100 atom

At 3rd half life = 100 atom/2 = 50 atom

At 4th half life = 50 atom/2 = 25 atom

Thus, 25 atoms are remained after 4 half lives.

Answer 2

25 atoms of the radioactive atoms will remain after 4 half lives.

    Given in the question,

• Initial amount of a radioactive element = 400 atoms
• Number of half lives = 4

Expression for the amount remaining of a radioactive element after 'n' half lives is given by,

$N=N_0(\frac{1}{2})^n$

Here, $N_0=$ Initial amount

$n=$ Number of half lives

By substituting the vales of $N_0$ and $n$ in the question,

$N=400(\frac{1}{2})^4$

   $=\frac{400}{16}$

   $=25$

        Therefore, 25 atoms of the radioactive atoms will remain after 4 half lives.

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