X^216 has half life of 5 days.The time taken for seven-eights of sample of x^210 to decay is
Answers
Fraction of the radioactive sample decayed= 7/8
Fraction of the radioactive sample uundecayed = 1 - 7/8 = ⅛
Number of days = 12
Undecayed fraction =⅛ =(½)³
Therefore half-life = 12 day/3 = 4 days
Verification:
In one half life undecayed fraction =1 × ½= 1/2 ( time taken =4 days= one half life)
In another half-life undecayed fraction = 1/2 × 1/2 = 1 (time taken = 4 days + 4 days = 8 days = 2 half-life)
In a further one half- life undecayed fraction = 1/4 × 1/2 = ⅛ ( time taken = 8 days + 4 days = 12 days).
Answer:
After 5 days 1/2 of the sample remains
After 10 days 1/2 * 1/2 = 1/4 remains
After 15 days 1/2 * 1/4 = 1/8 of the sample remains
or N = N0 e^-xt
N / N0 = 1/2 = e^-xt
ln .5 = -x * 5
x = .139
For 1/8 of the sample to remain N / N0 = .125
.125 = e^-.139 t
2.079 / .139 = t = 15