The half-life of is 245 days. After x days, 75% of original activity remained. The value of in days is ______. (Nearest integer) [Given: log 3 = 0.4771 and log 2 = 0.3010] [2026]

Question

The half-life of ${}^{65}{Zn}$ is 245 days. After x days, 75% of original activity remained. The value of $x$ in days is ______. (Nearest integer)

[Given: log 3 = 0.4771 and log 2 = 0.3010] [2026]

Smart Achievers · Accepted Answer

(102)

$t_{1 / 2} = \frac{l n 2}{K}$

$K = \frac{l n 2}{245}$

$t = \frac{1}{K} l n \frac{a_{0}}{a_{t}}$

$t_{25 %} = \frac{1}{K} l n \frac{4}{3}$

$t_{25 %} = \frac{1}{\frac{l n 2}{245}} l n \frac{4}{3}$

$t_{25 %} = 245 \cdot \frac{l n \frac{4}{3}}{l n 2} = 245 [\frac{2 \log 2 - \log 3}{\log 2}]$

$= 245 [\frac{2 \times 0.3010 - 0.4771}{0.3010}] = 101.66 day$

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