Question

The half life of radioactive potassium is 1.3 billion years. If 10 gram is present now,how much will be present in 100 years?

274

likes
1369 views

Answer to a math question The half life of radioactive potassium is 1.3 billion years. If 10 gram is present now,how much will be present in 100 years?

Expert avatar
Jon
4.6
108 Answers
Given:
- Half-life of radioactive potassium is 1.3 billion years.
- Initial amount of potassium is 10 grams.

Let's calculate how much will be present in 100 years.

The general formula to calculate the amount of radioactive substance remaining after a certain time is:
N(t) = N_{0} \times \left( \frac{1}{2} \right)^{\frac{t}{T_{\frac{1}{2}}}}
where:
- N(t) is the amount of the substance left after time t,
- N_{0} is the initial amount of the substance,
- t is the time that has passed,
- T_{\frac{1}{2}} is the half-life of the substance.

Given:
- Initial amount N_{0} = 10 grams
- Time t = 100 years
- Half-life T_{\frac{1}{2}} = 1.3 billion years = 1.3 \times 10^9 years

Plugging these values into the formula:
N(100) = 10 \times \left( \frac{1}{2} \right)^{\frac{100}{1.3 \times 10^{9}}}
N(100) = 10 \times \left( \frac{1}{2} \right)^{7.6923 \times 10^{-8}}
N(100) = 10 \times (0.999999999999923)^{7.6923 \times 10^{-8}}
N(100) \approx 10 \times 0.999999999999923 \approx 9.99999999999923 \text{ grams}

\boxed{9.99999999999923} grams of potassium will be present in 100 years.

Frequently asked questions (FAQs)
What is 0.2 as a percentage?
+
Math question: Find all positive integer solutions to the equation x^n + y^n = z^n, where n > 2, and x, y, z are integers.
+
What is the length of the hypotenuse of a right triangle if the two legs have lengths of 5 cm and 12 cm?
+
New questions in Mathematics
A=m/2-t isolate t
To calculate the probability that a player will receive the special card at least 2 times in 8 games, you can use the binomial distribution. The probability of receiving the special card in a single game is 1/4 (or 25%), and the probability of not receiving it is 3/4 (or 75%).
Pedro bought 9 kg of sugar at the price of R$1.80 per kilogram, six packets of coffee at the price of R$3.90 per packet and 8 kg of rice at the price of R$2.70 per kilogram. Knowing that he paid for the purchases with a R$100.00 bill, how much change did he receive?
Revenue Maximization: A company sells products at a price of $50 per unit. The demand function is p = 100 - q, where p is the price and q is the quantity sold. How many units should they sell to maximize revenue?
3x+5y=11 2x-3y=1
Determine the equations of the recipes that pass through the following pairs of points P1 (2;-1) and p2 (4;-1)
The ratio of tomatoes to red apples is 2:5. If there are 20 tomaoes in the garden, how many red apples are there?
B - (-4)=10
4x567
A National Solidarity Bond offers A 5 year bond offering a gross return of 15% Calculate the AER for this investment. (Give your answer to two decimal places, no need for the percent or € sign in your answer)
show step by step simplification: (¬𝑑∨((¬b∧c)∨(b∧¬c)))∧((𝑎 ∧ 𝑏) ∨ (¬𝑎 ∧ ¬𝑏))∧(¬𝑐∨((¬𝑑∧𝑎)∨(𝑑∧¬𝑎)))
3.24 ÷ 82
The points (-5,-4) and (3,6) are the ends of the diameter of the circle calculate subequation
A function is considered exponential when it has a base with positive values greater than zero and different from one, where the exponent is an unknown. An important characteristic of exponential functions is that they show rapid growth or decay as an independent variable increases or decreases. Given the function 25^(x+3)=125, it is calculated that x has the value of
At the dance there are 150 boys the rest are girls. If 65% are girls what is the total amount in the room
Congratulations, you have saved well and are ready to begin your retirement. If you have $1,750,000.00 saved for your retirement and want it to last for 40 years, and will earn 10.8% compounded monthly: What is the amount of the monthly distribuion? 216.50 How much interest is earned in retirement?
2X+2=8
When taking a test with m closed answers, a student knows the correct answer with probability p, otherwise he chooses one of the possible answers at random. What is the probability that the student knows the correct answer given that he answered the question correctly.
Oi👋🏻 Toque em "Criar Nova Tarefa" para enviar seu problema de matemática. Um dos nossos especialistas começará a trabalhar nisso imediatamente!
Question 3 A square has a perimeter given by the algebraic expression 24x – 16. Write the algebraic expression that represents one of its sides.