Select the number that would make this statement true: 628 divided by 0.628

Mathematics

1 answer:

Amiraneli [1.4K]3 years ago

8 0

The answer would be 10 to the third because if you divide that it would equal 1,000

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Dubnium-262 has a half-life of 34 s. How long will it take for 500.0 grams to

dmitriy555 [2]

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the time taken for the radioactive element to decay to 1 g is 304.8 s.

Step-by-step explanation:

Given;

half-life of the given Dubnium = 34 s

initial mass of the given Dubnium, m₀ = 500 grams

final mass of the element, mf = 1 g

The time taken for the radioactive element to decay to its final mass is calculated as follows;

$1 = 500 (0.5)^{\frac{t}{34}} \\\\\frac{1}{500} = (0.5)^{\frac{t}{34}}\\\\log(\frac{1}{500}) = log [(0.5)^{\frac{t}{34}}]\\\\log(\frac{1}{500}) = \frac{t}{34} log(0.5)\\\\-2.699 = \frac{t}{34} (-0.301)\\\\t = \frac{2.699 \times 34}{0.301} \\\\t = 304.8 \ s$

Therefore, the time taken for the radioactive element to decay to 1 g is 304.8 s.

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