Mathematics High School

The radioactive isotope 226Ra has a half-life of approximately 1599 years. There are 80g of 226Ra now.
(1) How much of it remains after 1,700 years? (Round your answer to three decimal places.)
(2) How much of it remains after 17,000 years? (Round your answer to three decimal places.)

Answers

Answer 1

1) 0.080 grams of 226Ra would remain after 17,000 years.

2) 44.000 grams of 226Ra would remain after 1,700 years.

To calculate the remaining amount of a radioactive isotope after a certain time, we can use the formula:

[tex]N(t) = N₀ * (1/2)^{(t / T_{ \frac{1}{2}} )}[/tex]

Where:

N(t) is the remaining amount of the isotope after time t.

N₀ is the initial amount of the isotope

[tex]T_{ \frac{1}{2} }[/tex] is the half-life of the isotope

Let's calculate the remaining amount of 226Ra for the given time periods:

(1) After 1,700 years:

[tex]N(t) = 80g * (1/2)^(1700 / 1599) \\ N(t) = 80g *(1/2)^(1.063165727329581) \\ N(t) ≈ 80g * 0.550 \\ N(t) ≈ 44.000g[/tex]

(rounded to three decimal places)

Therefore, approximately 44.000 grams of 226Ra would remain after 1,700 years.

(2) After 17,000 years:

[tex]N(t) = 80g * (1/2)^(17000 / 1599) \\ N(t) = 80g * (1/2)^(10.638857911194497) \\ N(t) ≈ 80g * 0.001 \\ N(t) ≈ 0.080g [/tex]

(rounded to three decimal places)

Therefore, approximately 0.080 grams of 226Ra would remain after 17,000 years.

Learn more about radioactive isotopes here,

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Answer:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Answer:

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Step-by-step explanation:

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Answers

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Answers

Answer:

D α H

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Step-by-step explanation:

Amount paid, D is directly proportional to the number of hotdogs, H

D = $3.50 per hot dog

D = $3.50 is directly proportional to 1 hotdog

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Answer:

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Step-by-step explanation:

Step-by-step explanation:

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Answers

Answer:

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Answers

Theorem 1. Pythagoras Theorem
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

Theorem 2. Thales Theorem
If a line is drawn parallel to one side of a triangle intersecting other two sides, then it divides the two sides in the same ratio.

Theorem 3. Euclid’s Theorem
Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers. It was first proved by Euclid in his work Elements.

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Theorem 5. Ceva’s Theorem
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Answers

Answer:

3

Step-by-step explanation:

on a number line, we use the absolute values to find the difference.

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the absolute value of -5 is 5

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so, the distance between -2 and -5 on a number line is 3

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Answers

a) 150 people
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Answers

Answer:

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Step-by-step explanation:

<3

Answer:the answer will be D)4.5

Step-by-step explanation:

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Answers

Answer:

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Answers

Answer:

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Step-by-step explanation:

Given:

Amount paid by a store for a set of spoons = $11

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answers

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Answers

Answer:

A

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

73 x 4 + 13 is 305

Answer:

305

explaination:

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Answers

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Answers

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

$3066.58

Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

Answer:

21

Step-by-step explanation:

Using inequality to solve this question, we say

Let the total number of newspapers sold be x

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Using your knowledge of mathematics, find the missing numbers in the
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Answers

Answer:

200,000 feet to dig

Step-by-step explanation:

We use a ratio for this problem

30,000         200,000,000

-----------   =   ---------------------

30                        x

200,000,000 * 30

----------------------------  = 200,000 feet to dig

30,000

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Answers

The simplified expression is c^5

Answer:

c^5

Step-by-step explanation:

:)

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