you have 400 grams (g) of a substance with a half life of 10 years. how much is left after 100 years?

Answers

Answer 1

After 100 years, there will be 6.25 grams of the substance remaining.

What is half life?

Half-life is the time it takes for half of the radioactive atoms in a sample to decay or for the concentration of a substance to decrease by half.

Amount remaining = initial amount x (1/2)^(number of half-lives)

In this case, half-life of the substance is 10 years, which means that after 10 years, half of the substance will have decayed. After another 10 years (20 years total), half of remaining substance will decay, leaving 1/4 of the original amount. After another 10 years (30 years total), half of that remaining amount will decay, leaving 1/8 of the original amount. This process continues every 10 years.

To find the amount of substance remaining after 100 years, we need to know how many half-lives have occurred in that time: 100 years / 10 years per half-life = 10 half-lives

Amount remaining = 400 g x (1/2)¹⁰= 6.25 g

Therefore, after 100 years, there will be 6.25 grams of the substance remaining.

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Related Questions

a 1.25 g sample of co2 is contained in a 750. ml flask at 22.5 c. what is the pressure of the gas, in atm?

Answers

The pressure of gas is 1.05 atm when a 1.25 g sample of CO₂ is contained in a 750ml flask at 22.5°C.

Molecular weight of CO₂ is 1.25g ,Volume of CO₂ is 750ml,Temperature of CO₂ is 22.5°C and the gas constant is 0.08206 L atm/mol K.

Using the ideal gas law equation the pressure is found to be 1.05 atm.

To calculate the pressure of the gas, we can use the ideal gas law equation: [tex]PV=nRT[/tex]
Where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
First, we need to convert the volume to liters by dividing by 1000: 750 ml = 0.75 L.
Next, we need to calculate the number of moles of CO₂ present in the flask. We can use the molecular weight of CO₂ to convert from grams to moles:

[tex]1.25 * (1 /44.01 ) = 0.0284 mol[/tex]
Now we can plug in the values into the ideal gas law equation:

[tex]PV=nRT[/tex]
[tex]P * 0.75 L = 0.0284 mol * 0.08206 L*atm/mol*K * (22.5 + 273.15) K[/tex]
Simplifying and solving for P, we get:
[tex]P = (0.0284 * 0.08206 * 295.65) / 0.75 = 1.05 atm[/tex]
Therefore, the pressure of the gas in the flask is 1.05 atm.

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