The half-life of ⁶⁵Zn 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)

The half-life of 65Zn is 245 days. After x days, 75% of original activity remained. The value of x in days is

Q. The half-life of ⁶⁵Zn 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)

Correct Answer: 102

Explanation

Radioactive decay follows the relation:

A = A₀ (1/2)^{t / t_1/2}

Here, half-life t_1/2 = 245 days.

75% activity remaining means:

A / A₀ = 0.75 = 3/4

Substitute in decay equation:

3/4 = (1/2)^{t / 245}

Taking logarithm on both sides:

log(3/4) = (t / 245) log(1/2)

Using log values:

log(3/4) = log 3 − log 4 = 0.4771 − 2(0.3010) = −0.1249

log(1/2) = −0.3010

Substitute:

−0.1249 = (t / 245)(−0.3010)

Solve for t:

t = (0.1249 / 0.3010) × 245 ≈ 101.6 ≈ 102 days

Hence, the required value of x is 102 days.

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