Examkin

Soru

Zorluk: KolayRadioactive Decay Law and Half-life

A radioactive isotope has a half-life of 5 days5\text{ days}. If the initial activity of a sample of this isotope is 400 Bq400\text{ Bq}, what is the activity of the portion of the sample that has decayed after 15 days15\text{ days}?

  1. 350 Bq350\text{ Bq}Cevap
  2. B
    50 Bq50\text{ Bq}
  3. C
    100 Bq100\text{ Bq}
  4. D
    300 Bq300\text{ Bq}

Cevap

350 Bq350\text{ Bq}
After 3 half-lives (15 days), one-eighth of the original activity remains, which equals 50 Bq. Therefore, seven-eighths of the original activity has decayed, giving 400 Bq - 50 Bq = 350 Bq.

Adım Adım Çözüm

1
Calculate the number of half-lives that elapse in 15 days
Number of half-lives, n=15 days5 days=3n = \frac{15\text{ days}}{5\text{ days}} = 3
Dividing the total time elapsed by the half-life period yields the number of decay half-lives.
2
Calculate the remaining activity of the sample
Remaining activity A=A0(12)n=400×(12)3=400×18=50 BqA = A_0 \left(\frac{1}{2}\right)^n = 400 \times \left(\frac{1}{2}\right)^3 = 400 \times \frac{1}{8} = 50\text{ Bq}
The remaining fraction after nn half-lives is (1/2)n(1/2)^n of the initial activity.
3
Subtract the remaining activity from the initial activity to find the decayed activity
Decayed activity Adecayed=A0−A=400 Bq−50 Bq=350 BqA_{\text{decayed}} = A_0 - A = 400\text{ Bq} - 50\text{ Bq} = 350\text{ Bq}
The portion that has decayed is equal to the total initial activity minus the activity that remains.

Anahtar Kavram

Distinction between remaining activity and decayed activity in radioactive decay calculations
Bu soruyu puanla

Konular

Radioactive Decay Law and Half-life

Bu konudan daha fazla soru