What is the half‑life of an isotope that decays to 25% of its original activity in 85.6 h

42.9 h

Explanation:

From the question given above, the following data were obtained:

Original amount (N₀) = 100%

Amount remaining (N) = 25%

Time (t) = 85.8 h

Half-life (t½) =?

Next, we shall determine the number of half-lives that has elapse. This can be obtained as follow:

Original amount (N₀) = 100%

Amount remaining (N) = 25%

Number of half-lives (n) =?

N = 1/2ⁿ × N₀

25 = 1/2ⁿ × 100

Cross multiply

25 × 2ⁿ = 100

Divide both side by 25

2ⁿ = 100/25

2ⁿ = 4

Express 4 index form with 2 as the base

2ⁿ = 2²

n = 2

Thus, two half-lives has elapsed.

Finally, we shall determine the half-life of the of the isotope. This can be obtained as follow:

Time (t) = 85.8 h

Number of half-lives (n) = 2

Half-life (t½) =?

n = t / t½

2 = 85.8 / t½

Cross multiply

2 × t½ = 85.8

Divide both side by 2

t½ = 85.8 / 2

t½ = 42.9 h

Thus, the half-life of the of the isotope is 42.9 h

it can be observed without changing the identity of the object.

it depends on what substance you're talking about as well as many other factors. in quantum mechanics, the observation of particles affects the observers ability to measure certain properties. for example: you can know the velocity of a particle, but you can't know it's position; or you can know it's position, but not it's velocity. it's like trying to find out where a grain of sand is by throwing other grains of sand at it. once you find out where it is, it's been moved. it's also like trying to find an answer to the question of whether or not a tree falling in a forest makes a sound if nobody is there to hear it. paradoxically, the only way to find out is to be there and hear it.