# A radioactive sample initially contains N atoms…

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A.7?/8

B.3N/8

C. 5?/8

D. ?/8

A

## DETAILS…

After first half-life, N/2 will remain.

After second half-life, N/2/2 = N/4 will remain

After third half-life, N/4/2 = N/8 will remain

If N/8 remains, the number of atoms that must have disintegrated = N – N/8

= 8N/8 – N/8 = (8N – N)/8 = 7N/8

### Now for the right answer to the above question:

1. Option A is correct.
2. Option B is incorrect.
3. C is incorrect.
4. D is not the correct answer.

## KEY-POINTS

• After each half-life, half of the preceding number of atoms will remain.
• The number that must have decayed can be calculated by subtracting the remaining number of atoms from the original number.
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/ culled from 2016 JAMB-UTME physics past question 32 /

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