Radioactive isotope X has a half-life of 500,000 years. This isotope may be found in some types of volcanic rocks. A particular sample of volcanic rock taken from a layer that covered up some of the earliest known human-like footprints contains 0.125 mg of isotope X. The volcanic rock sample originally contained 8.00 mg of isotope X. How long ago were these footprints made. I need the equation. Thanks. please I am stuck on this question. PLEASE
Answer:
The age of the earliest known human-like footprints is approximately 3000000 years.
Explanation:
Decay of isotopes is represented by the following ordinary differential equation:
[tex]\frac{dm}{dt} = -\frac{m}{\tau}[/tex] (Eq. 1)
Where:
[tex]\frac{dm}{dt}[/tex] - First derivative of mass with respect to time, measured in miligrams per year.
[tex]m[/tex] - Current mass of the isotope, measured in miligrams.
[tex]\tau[/tex] - Time constant, measured in years.
Now we proceed to obtain the solution of the differential equation:
[tex]\int\limits {\frac{dm}{m} } = -\frac{1}{\tau}\int dt[/tex]
[tex]\ln m = -\frac{t}{\tau}+C[/tex]
[tex]m(t) = e^{-\frac{t}{\tau}+C }[/tex]
[tex]m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex] (Eq. 2)
Where:
[tex]m_{o}[/tex] - Initial mass of the isotope, measured in miligrams.
[tex]t[/tex] - Time, measured in years.
[tex]\tau[/tex] - Time constant, measured in years.
We proceed to clear time within the formula presented above:
[tex]\ln \frac{m(t)}{m_{o}} = -\frac{t}{\tau}[/tex]
[tex]t = -\tau \cdot \ln \frac{m(t)}{m_{o}}[/tex]
In addition, time constant can be found as a function of half-life:
[tex]\tau = \frac{t_{1/2}}{\ln 2}[/tex] (Eq. 3)
If we know that [tex]t_{1/2} = 500000\,yr[/tex], [tex]m_{o} = 8\,mg[/tex] and [tex]m(t) = 0.125\,mg[/tex], the age of the earliest known human-like footprints is:
[tex]\tau = \frac{500000\,yr}{\ln 2}[/tex]
[tex]\tau \approx 721347.520\,yr[/tex]
[tex]t = -(721347.520\,yr)\cdot \ln \left(\frac{0.125\,mg}{8\,mg} \right)[/tex]
[tex]t \approx 3000000\,yr[/tex]
The age of the earliest known human-like footprints is approximately 3000000 years.
I NEED HELP ASAP!!
Scientific Inquiry
Science is the investigation of the ______________ ________________. Biology is the branch of science that studies ___________ _______________ and the environments they live in.
The Scientific Method
The scientific method is a __________________ used during a scientific ____________________ to answer a scientific question.
• Qualitative data is something that can’t be
________________ but can change over time.
Scientific inquiry can’t answer questions about a person’s beliefs, ethics, _________________, and feelings.
Which of these are questions that science can answer?
A. Was the flu vaccine more effective this year than last year?
B. Is it ethical to use stem cells in human research?
C. Does a drop in temperature affect the number of offspring that frogs produce?
D. Will people feel better if they eat organic produce instead of conventionally grown produce?
E. Are coffee drinkers worried about their heart disease risk?
Construct Hypotheses and Predictions
A hypothesis is a plausible __________________ for a particular fact. The hypothesis needs to be ____________________ or ____________________ based on collected evidence. All studies must have at least one hypothesis.
Answer:
Science is the investigation of the ______________ ________________. Biology is the branch of science that studies living organisms and the environments they live in.
The scientific method is a tool used during a scientific investigation to answer a scientific question.
• Qualitative data is something that can’t be
collected but can change over time.
Scientific inquiry can’t answer questions about a person’s beliefs, ethics, values, and feelings.
im going to say d
Construct Hypotheses and Predictions
A hypothesis is a plausible guess for a particular fact. The hypothesis needs to be supported or refuted (proven wrong) based on collected evidence. All studies must have at least one hypothesis.
Which statement best explains how the passage fits
the realistic fiction genre?
Answer:
It seems believable and familiar.
Explanation:
Plz mark Brainlest
Pls fill in the blank
Because it can either lose or share electrons when it combines with has some of the properties of metals and
other elements, each has some of the properties of nonmetals.
A. Metalloids
B. Sodium
C. Gold
A. Metalloids
They can either lose an electron or share an electron when it combines with other elements. They have some properties of metals and some properties of non-metals.
The solution starts with increased ________________
Answer:
Concentration
Explanation:
Answer:
concintracion
Explanation:
How many fluorine atoms are present in 6.30 g of C2F4
Fluorine atoms = 1.517 x 10²³
Further explanationThe mole is the number of particles contained in a substance
1 mol = 6.02.10²³
Moles can also be determined from the amount of substance mass and its molar mass
[tex]\large{\boxed{\boxed{\bold{mol=\frac{mass}{molar\:mass}}}}[/tex]
Proust stated the Comparative Law that compounds are formed from elements with the same Mass Comparison so that the compound has a fixed composition of elements
Mass of F[tex]\tt mass~F=\dfrac{4.Ar~F}{MW~C_2F_4}\times mass~C_2F_4\\\\mass~F=\dfrac{4.19}{100}\times 6.3=4.788~gr[/tex]
mol of F[tex]\tt =\dfrac{4.788}{19}=0.252[/tex]
number of Fluorine atoms[tex]\tt 0.252\times 6.02\times 10^{23}=1.517\times 10^{23}[/tex]
Which of the following is NOT an example of a homogeneous mixture? a oxygen b tea c water d pizza
A student dissolved a 0.139g sample of oxalic acid, H2C2O4, in water in an Erlenmeyer flask. Then the student titrated the H2C2O4 solution in the flask with a solution of KMnO4, which has a dark purple color. The balanced chemical equation for the reaction that occurred during the titration is shown above. (a) Identify the species that was reduced in the titration reaction. Justify your answer in terms of oxidation numbers.
Answer:
MnO4 − was reduced
C2 O4^2- was oxidized
Explanation:
2MnO4 −(aq) +5H +(aq) +2 C2 O4^2-(aq) +6H+(aq) →2Mn2+(aq) + 10CO2(g) +8H2 O(l)
A redox reaction is characterized by a change in the oxidation number of reacting species from left to right in the reaction equation.
If we look at Manganese, its oxidation number was decreased from +7 on the left hand side to +2 on the right hand side. This implies that it gained five electrons. recall that reduction refers to electron gain.
If we look at carbon, its oxidation number increased from +3 on the left hand side to +4 on the right hand side. This indicates loss of one electron and oxidation refers to electron loss.
MnO₄⁻ was reduced and C₂O₄²⁻ was oxidized in the titration.
The balanced chemical equation for the reaction can be expressed as:
[tex]\mathbf{6H^+_{(aq0} + 2MnO_4^-_{(aq)} + 5H_2C_2O_4 _{(aq)} \to 10CO_{2(g)} +8H_2O_{(l)} + 2Mn^{2+}_{(aq)}}[/tex]
A redox reaction can be described by a variation in the oxidation number of reacting species in the chemical reaction equation from the reactant side to the product side
Oxidation takes place when a substance(atom, molecule, or compound) loses an electronReduction occurs when a substance gains an electron.Let consider Mn in MnO₄⁻, its oxidation number was decreased from +7 on the reactant side to +2 on the product side. This shows a gain of additional five electrons.
Thus, MnO₄⁻ is reduced.
Also in C₂O₄²⁻, the oxidation number of carbon increases from +3 on the reactant side to +4 on the product side. Since an electron is lost, then oxidation occurs at C₂O₄²⁻
Learn more about oxidation and reduction here:
https://brainly.com/question/13699873?referrer=searchResults
What is a polar molecule?
A. A molecule with symmetrical polar covalent bonds
B. A molecule with symmetrical nonpolar covalent bonds
C. A molecule with a negative pole and a positive pole
D. A molecule with two atoms of the same electronegativity
Explanation:
A molecule with a negative pole and a positive pole is called a polar molecule.
(d) A molecule with two atoms of the same electronegativity
What is meant by a polar molecule?A polar molecule is usually formed when the one end of the molecule is said to possess more positive charges and whereas the opposite end of the molecule has negative charges, creating an electrical pole.
What is a polar molecule example? Water (H2O) is a polar molecule. The bonds between hydrogen and oxygen are distributed so that the hydrogen atoms are both on one side of the oxygen atom rather than evenly spaced.Sodium Chloride (NaCl) which is an ionic compound acts as a polar molecule. Usually, the large difference in electronegativities in sodium and chlorine makes their bond polar.Learn more about polar molecule on https://brainly.com/question/11405437
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Pleaseee help ASAP
will mark brainliest!!! <3
Answer:
Fluorine belongs to the group 7 A so it must have 7 electrons in the oribits so the answer would be A as u count the electrons in the orbits, There are exactly 7 electron
Explanation:
Explain the term rate of a chemical reaction.
Answer:
The rate of a reaction is a measure of how quickly a reactant is used up, or a product is formed.
Explanation:
The nucleus is held closely together by?
The nucleus of an atom is held together by the strong nuclear force to hold together protons and neutrons. The strong nuclear force is stronger than electricity and gravity. It's even the strongest out of the four fundamental forces.
The atomic mass of an atom is calculated by adding up what two subatomic particles
The atomic mass of an atom is calculated by adding up protons and neutrons
Further explanationThere are two components that accompany an element, the mass number and atomic number
Atoms are composed of 3 types of basic particles (subatomic particles): protons, electrons, and neutrons
The charge of 1 proton is equal to a charge of 1 electron but has a different sign
The proton is positively charged (+1), the electron is negatively charged (-1). and neutrons not charged (neutral)
The Atomic Number (Z) indicates the number of protons and electrons in an atom of an element.
Atomic number = number of protons = number of electrons ⇒ neutral number
Atomic mass is the sum of protons and neutrons
Atomic Number (Z) = Atomic mass (A) - Number of Neutrons
Where in equation for photosynthesis does carbon dioxide belong
Answer:
The equation for photosynthesis is 6 CO2 + 6 H2O + light --> C6H12O6 + 6 O2, so carbon dioxide will be found in the reactant part of the equation.
i need help ' please
Answer:
s orbitals - spherical shape
p orbitals - dumbbell shape
d orbitals- dxy, dyz , dzx -double dumbbell
- dx²-y²- double dumbbell (along axis)
-dz² -dumbbell with electron cloud
( along the axis)
therefore here the answer is 2s and 3s
i need help Which of the following shows the correct order in which organs take part in the process of digestion
Answer:
Mouth
Esophagus
Stomach
The small intestine
Colon (large intestine)
Rectum
Which type of fault is under compression? A. Normal. B. Thrust. C. Transform. D. Strike-slip
Answer:
The answer is Thrust
A train travels at an average speed of 25 miles per hour. How long does it take the train to travel 2000 miles?
nevermind. I was wrong. I didn't see the other answers
.) If a solution had a pH level of 13.2, it would be considered a:
O A. strong base
O B. weak base
O C. strong acid
O D. weak acid
What is the charge of protons?
Answer:
protons naturally have the charge of +1
Answer:Protons have a positive electrical charge of one (+1) and a mass of 1 atomic mass unit (amu), which is about 1.67×10−27 kilograms
Explanation:
Why can astronauts jump so high, and "hang" so
long, on the moon?
gravity is stronger on the earth, and gravity is what brings you back down
so, if there's less gravity, then there's more air time
Answer:
Low gravity
Explanation:
The moon has lower gravity than Earth, therefor when someone jumps, they will not return to the surface automatically.
What are some of the regulations about cell phone waste?
Are the regulations the same everywhere, which countries have different regulations?
New technology to reduce waste?
Pls and thank you!
What are some of the regulations about cell phone waste?
In general, companies take part in the responsibility of taking back the e-waste resulted from their products.
Are the regulations the same everywhere, which countries have different regulations?
In 2005, two important directives were published in the European Union. The first stipulates that: 1) all manufacturers selling electrical and electronic equipment in and to EU countries label the equipment to inform customers that it must be recycled and 2) make sure that their products are properly disposed of or recycled after the life cycle. The second requires manufacturers to eliminate or minimize the use of lead, mercury, hexavalent chromium, cadmium, polychrome and diphelin biphenyl ethers in electrical and electronic equipment sold in the EU after 1 July 2006.
New technology to reduce waste?
Companies are trying to reduce the amount of resources needed in order to create their products. One alternative is the modular smarthphones, which aims to reduce the amount of e-waste of the phone by only upgrading a few elements of hardware.
HELP PLEASE!!!
chemistry question
Answer:
Its going to be D) In sigma bonds the electrons are in the space between the joined atoms and pi bonds above and below the joined atoms
which of the following lists contains only elements?
A ) air , water,oxygen
b) hydrogen, oxygen, brass
c) air , fire , water, earth
d) calcium, sulphur, carbon
Which of the following electromagnetic waves has the most energy on the electromagnetic spectrum?
O A Infrared
O B. X-ray
O C. Gamma
O D. Radio
Answer:
Gamma rays
Explanation:
The waves with higher frequencies will have higher energies and gamma waves have the highest frequencies on electromagnetic scale ,because of this reason gamma waves is the answer.
Which chemical equation best represents the Law of Conservation of
Mass?
O H+ 0 -> H20
H2 + 02 --> H20
2H2 + O2 --> 2H20
H2 + O2 --> 2H,02
2H₂ + O₂ ⇒ 2H₂O
Further explanationConservation of mass states that
In a closed system, the masses before and after the reaction are the same
So it can be concluded
mass of the reactants = mass of the productsmass cannot be created or destroyedThe number of atoms involved in a reaction remains the same⇒ number of moles also the samechemical equation in balanced formSo let's see which of the several options , which one has the same number of atoms on both sides of the equation
2H₂ + O₂ ⇒ 2H₂O
H ⇒ left 4, right 4
O ⇒ left 2, right 2
so the equation is in balance and represents the Law of Conservation of
Mass
Convert the following to Kelvin
12) 0° C
13) -50° C
14) 90° C
15) -20° C
Answer:
12)273.15 kelvin
13)223.15 kelvin
14)363.15 kelvin
15)253.15 kelvin
Explanation:
thank u!!!
Answer:
12) 273.15
13) 223.15
14) 363.15
15) 253.15
Explanation:
Formula:
_C+273.15=_K
What is the importance of protons ?
Protons are important because they help keep the nucleus together, they also attract negatively charged electrons and keep them in orbit around the nucleus.
What kind of reaction happens when two compounds switch elements? Apex
Answer:
A replacement reaction occurs when elements switch places in compounds. This type of reaction involves ions. Generally, more reactive elements replace less reactive elements. A single replacement reaction occurs when one element replaces another element in one compound.
Explanation:
Just figured it out!
Answer: a double - replacement reaction
Explanation:
I just got it right on Apex
During a scientific investigation, which step will a scientist perform first?
Answer:
you need to have a question or a problem first