A piece of charcoal used for cooking is found at the remains of an ancient campsite. a 0.94 kg sample of carbon from the wood has an activity of 1580 decays per minute. find the age of the charcoal. living material has an activity of 15 decays/minute per gram of carbon present and the half-life of 14c is 5730 y. answer


Answer 1
Answer: Mass of sample of charcoal = 0.94 kg = 0.00094 

∴, activity = decay rate / mass = 1580/0.00094
                                                 = 1.681 X 10^6 decays per min per gram

Using the half-life formula, we have: 
activity of sample / activity of modern carbon = (1/2)^(age / half-life) 
∴, Age = half-life x log (base 2) (modern activity / coal activity)
           = 5730 x log(base 2)(1.681X10^6/ 15)
           = 96115 years.

Answer: Age of the charcoal = 96115 years
Answer 2

Final answer:

Using the radiocarbon dating technique and applying the decay formula, it is calculated that the age of the charcoal from the an ancient campsite is approximately 9,500 years.


The age of the charcoal can be found using the technique of radiocarbon dating, which capitalizes on the process of radioactive decay. The isotope carbon-14 (¹4C) is used in this method as it has a known half-life of 5730 years. The number of decays per minute per gram of carbon in a live organism is known as its activity.

Initially, the activity was given as 15 decays per minute per gram. The present activity of the carbon in the charcoal is provided at 1580 decays per minute for a 0.94 kg or 940 gram sample. Thus, the current activity per gram is 1580/940 equals approximately 1.68 decays per minute per gram.

Given that the half-life of ¹4C is 5730 years, we can apply the formula for calculating the time passed using the rate of decay, which is given as T = (t1/2 / ln(2)) * ln(N0/N), where 'ln' is the natural logarithm, 'N0' is the initial quantity (15 decays/minute per gram), 'N' is the remaining quantity (1.68 decays/minute per gram).

Plugging in the given values, we get T = (5730 / ln(2)) * ln(15/1.68), which gives us approximately 9,500 years. Therefore, the age of the charcoal is around 9,500 years.

Learn more about Radiocarbon Dating here:



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is due to the (4). in the leave that allows the plant to absorb
sunlight. Plants use the light energy in a reaction called (5).
where they make food in the form of sugar and produce oxygen.
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Answer: 4 chlorophyll    5 and photosynthesis  6 sugar glucose

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During an experiment, a student adds 2.90 g CaO to 400.0 mL of 1.500 M HCl . The student observes a temperature increase of 6.00 °C . Assuming that the solution's final volume is 400.0 mL , the density is 1.00 g/mL , and the heat capacity is 4.184 J/g⋅°C , calculate the heat of the reaction, ΔHrxn .



ΔHrxn = 193107.69 J/mol


ΔHrxn = mcΔT

m = mass

c = heat capacity

ΔT = temperature variation

density = m/V

m = density x V

m = 1.00 g/mL x 400.0 mL

m = 400.0 g

ΔHrxn = mcΔT

ΔHrxn = 400 g x 4.184 J/g°C x 6.00 °C

ΔHrxn = 10041.6 J

CaO + 2HCl  → CaCl₂ + H₂O

CaO = 56.0774 g/mol

2.90 g CaO = 0.052 mol

400.0 mL of 1.500 mol/L HCl = 0.6 mol HCl

ΔHrxn = 10041.6 J is for 0.052 mol of CaO

ΔHrxn = 193107.69 J is for 1 mol of CaO

Which of the following is true for the quantum mechanical atomic model? A. Atoms absorb or emit electrons from the nucleus when they interact with electromagnetic radiation.

B. Every atom absorbs all wavelengths of light energy or electromagnetic radiation.

C. Electrons give off electromagnetic radiation when they jump from a high to a low energy level.

D. Electrons are perfectly evenly distributed throughout the atom.​​


Answer: C. Electrons give off electromagnetic radiation when they jump from a high to a low energy level.


 Electrons give off electromagnetic radiation when they jump from a high to a low energy level in the quantum mechanical atomic model. This is known as the emission spectrum of an atom, and each element has its unique emission spectrum. This phenomenon was explained by the Bohr model of the atom and is a fundamental concept of the quantum mechanical atomic model.

 Option A is incorrect because atoms cannot absorb or emit electrons from the nucleus when they interact with electromagnetic radiation. Option B is also incorrect because atoms only absorb certain wavelengths of light energy or electromagnetic radiation, which corresponds to the energy difference between electron energy levels. Option D is incorrect because electrons are not evenly distributed throughout the atom in the quantum mechanical atomic model; instead, they occupy specific energy levels or orbitals.

Consider the titration of a 73.9 mL sample of 0.13 M HC2H3O2 with 6.978 M NaOH. Ka(HC2H3O2) = 1.8x10-5 Determine the initial pH before any NaOH is added. Express your answer using two decimal places.Consider the titration of a 46.6 mL sample of 0.078 M HC2H3O2 with 1.135 M NaOH. Ka(HC2H3O2) = 1.8x10-5 Determine the volume of added base required to reach the equivalence point. Answer in units of milliliters.

Consider the titration of a 17.2 mL sample of 0.128 M HC2H3O2 with 0.155 M NaOH. Ka(HC2H3O2) = 1.8x10-5 Determine the pH at 0.46 mL of added base.



1. pH = 2,82

2. 3,20mL of 1,135M NaOH

3. pH = 3,25


The buffer of acetic acid (HC₂H₃O₂) is:

HC₂H₃O₂ ⇄ H⁺ + C₂H₃O₂⁻

The reaction of HC₂H₃O₂ with NaOH produce:

HC₂H₃O₂ + NaOH → C₂H₃O₂⁻ + Na⁺ + H₂O

And ka is defined as:

ka = [H⁺] [C₂H₃O₂⁻] / [HC₂H₃O₂] = 1,8x10⁻⁵ (1)

1. When in the solution you have just 0,13M HC₂H₃O₂ the concentrations in equilibrium will be:

[H⁺] = x

[C₂H₃O₂⁻] = x

[HC₂H₃O₂] = 0,13 - x

Replacing in (1)

[x] [x] / [0,13-x] = 1,8x10⁻⁵

x² = 2,34x10⁻⁶ - 1,8x10⁻⁵x

x² - 2,34x10⁻⁶ + 1,8x10⁻⁵x  = 0

Solving for x:

x = - 0,0015 (Wrong answer, there is no negative concentrations)

x = 0,0015

As [H⁺] = x = 0,0015 and pH is -log [H⁺], pH of the solution is 2,82

2. The equivalence point is reached when moles of HC₂H₃O₂ are equal to moles of NaOH. Moles of HC₂H₃O₂ are:

0,0466L × (0,078mol / L) = 3,63x10⁻³ moles of HC₂H₃O₂

In a 1,135M NaOH, these moles are reached with the addition of:

3,63x10⁻³ moles × (L / 1,135mol) = 3,20x10⁻³L = 3,20mL of 1,135M NaOH

3. The initial moles of HC₂H₃O₂ are:

0,0172L × (0,128mol / L) = 2,20x10⁻³ moles of HC₂H₃O₂

As the addition of NaOH spent HC₂H₃O₂ producing C₂H₃O₂⁻. Moles of C₂H₃O₂⁻ are equal to moles of NaOH and moles of HC₂H₃O₂ are initial moles - moles of NaOH. That means:

0,46x10⁻³L NaOH × (0,155mol / L) = 7,13x10⁻⁵ moles of NaOH ≡ moles of C₂H₃O₂⁻

Final moles of HC₂H₃O₂ are:

2,20x10⁻³ - 7,13x10⁻⁵ = 2,2187x10⁻³ moles of HC₂H₃O₂

Using Henderson-Hasselbalch formula:

pH = pka + log₁₀ [C₂H₃O₂⁻] / [HC₂H₃O₂]

Where pka is -log ka = 4,74. Replacing:

pH = 4,74 + log₁₀ [7,13x10⁻⁵] / [2,2187x10⁻³ ]

pH = 3,25

I hope it helps!

The theoretical yield for CuCO3.Cu(OH)2+2h2SO4 ®2CuSO4+2H2O+3CO2



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