At 45°C, dinitrogen pentoxide (N2O5) decomposes into nitrous dioxide (NO2)and oxygen (O2) according to the law of uninhibited decay. An initial amount of 0.25 mole of dinitrogen pentoxide decomposes to 0.15 mole in 17 minutes. How much dinitrogen pentoxide will remain after 30 minutes? Howlong will it take until 0.01 mole of dinitrogen pentoxide remains?

Q: The radioactive element​ carbon-14 has a​ half-life of 5750 years. A scientist determined that the…

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Q: After 5.5 days, a 100 mg sample of radon-222 decayed to 37 mg. (a) Find a formula for m(t), the mass…

A: GIVEN After 5.5 days, a 100 mg sample of radon-222 decayed to 37 mg. We need to find (a) Find a…

Q: The​ half-life of​ carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree…

A: Given that the​ half-life of​ carbon-14 is 5600 years and if a piece of charcoal made from the wood…

Q: Under certain water conditions, the free chlorine (hypochlorous acid, HOCI) in a swimming pool…

A: The formula  N(t) = No e(-kt)  models this decay process well, where   t     = time measured in…

Q: An element with mass 140 grams decays by 21.6% per minute. How much of the element is remaining…

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Q: An element with mass 730 grams decays by 28.8% per minute. How much of the element is remaining…

A: There is an exponential decay with rate of 28.8%.

Q: A small metal bar, whose initial temperature is 25°C'is dropped into a large container of boiling…

A: Given that :- Initial Temperature of Metal Bar=25°C Temperature of boiling water=100°C How long will…

Q: A bacteria population grows by 10% every 3 days. Based on this, if we initially have 2,000…

A: First of all we should know that the growth is exponential so formula will be: Nd = N0ekd where N0…

Q: Under certain water conditions, the free chlorine (hypochlorous acid, HOCI) in a swimming pool…

A: Given that the amount of free chlorine to be 2.4 parts per million.Twenty four hours later the…

Q: The half-life of the radioactive element tritium is 12 years. Find its decay constant.

A: We have, the half-life of the radioactive element tritium is 12 years. As we know that, The time in…

Q: Under certain water conditions, the free chiorine (hypochlorous acid /HOCI) in a swimming pool…

A: This question can be solved using the law of uninhibited decay according to which  A=A0ekt

Q: If a piece of charcoal made from wood of a tree shows only 62% of the carbon 14 expected living in…

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Q: A sample of tritium-3 decayed to 85% of its original amount after 4 years. How long would it take…

A: Given problem:- A sample of tritium-3 decayed to 85% of its original amount after 4 years. How long…

Q: How much should be invested at a rate of 7% coumpounded continuously to produce an amount of $15,000…

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Q: A Plane (Plane A) travels North at a speed of 800 kph. after 15 minutes, another plane (plane B)…

A: Planes are moving same direction :

Q: There are 5,000 wolves in the park, but their population is expected to decay at a rate of 8% per…

A: Given, initially , wolves in the park = 5000 Decay of population = 8% per year finally , wolves in…

Q: The half-life of carbon-14, 14C, is approximately 5,730 years. A bone fragment is estimated to have…

A: Given information: Initial amount=Q0=7 mgHalf life=t12=5730 years

Q: A certain substance decays so that each year 92% of the previous year's material is still present.…

A: A substance decay such that each year 92% of the previous year's material still remains. So, 8% of…

Q: A sample of a newly discovered element, West Virginium, has a half-life of 295 years. How long will…

A: We have to find out t

Q: The amount remaining of a 162 mL sample of a liquid substance, y (in mg) after x hours is modeled by…

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Q: A freshly brewed cup of coffee is set on the counter and has a temperature of 200° Fahrenheit. After…

A: Let us assume that hot coffee is poured at time t=0 Given:   Initial temperature at  t=0, T=200°F…

Q: A body of unknown temperature is placed in a refrigerator at a constant temperature of 0° F. If…

A: Given:- A body of unknown temperature is placed in a refrigerator at a constant temperature of 0° F.…

Q: A body of an unknown temperature is placed in a room which is held at a constant temperature of 30 .…

A: Given that, A body of an unknown temperature is placed in a room which is held at a constant…

Q: Under certain water​ conditions, the free chlorine​ (hypochlorous acid,​ HOCl) in a swimming pool…

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Q: The half-life of a substance is 24 hours. About how many hours will it take for 6 grams to decay to…

A: SOLUTION

Q: Strontium-90 has a half-life of 29 years. Beginning with a 10 mg sample, find how long it takes for…

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Q: A small metal bar, whose initial temperature was 20° C, is dropped into a large container of boiling…

A:

Q: Under certain water conditions, the free chlorine (hypochlorous acid, HOCI) in a swimming pool…

A: According to the decay law/uninhibited decay law:  A=A0 ek·t, where A0 is the initial amount. Given:…

Q: The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000…

A: Given:The initial number of mosquitoes is 1000. That is, P0 = 1000.The numbr of  mosquitoes is 1600…

Q: A certain radioactive isotope has a half-life of approximately 1750 years. How many years to the…

A: Consider the amount is, A=Pert here, A is the isotope, P is the initial amount and r is the…

Q: At the beginning of an experiment, a scientist has 228 grams of radioactive goo. After 135 minutes,…

A: Given that: P=the initial amount= 228 Time=t=135 minutes A=final amount= 3.5625 r=rate    Using the…

Q: 1. Strontium-90, 90Sr, has a half-life of 29 years. a) If 42.5 grams remain after 50 years, what is…

A: The formula for the quantity remaining of a substance after t years is: Nt=N012tt12 Here, t12=…

Q: A lighthouse, L, is on an island 8 mi away from the closest point, P, on the beach. If the…

A: Given: A lighthouse rotates clockwise at a constant rate of 17 revolutions/min.

Q: Of an initial amount of 4000 g of lead-210, how much will remain in 190 years? Lead-210 decays at a…

A: Here initial amount A0=4000g Decaying rate λ= 3.15% = 0.0315 Let amount remains in 190 years= A(t)

Q: The radioactive element carbon-14 has a half life of 5750 years. A scientist determined that the…

A: Given:The radioactive element carbon-14 has a half-life of 5750 years and the bones from a mastodon…

Q: A lighthouse, L, is on an island 4 mi away from the closest point, P, on the beach. If the…

A:

Q: A certain element decays at a rate of .000163/year. Of a piece of this element of 450 kg, how much…

A:

Q: Element X decays radioactively with a half life of 9 minutes. If there are 170 grams of Element X,…

A: Given- Element X decays radioactively with a half life of 9 minutes and there are 170 grams of…

Q: An element with mass 820 grams decays by 26.8% per minute. How much of the element is remaining…

A: We have to use exponential decay function to solve the problem

Q: Only 25% of the carbon-14 in a wooden bowl remains. How old is the bowl? (Carbon-14 has a half-life…

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Q: alf-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only…

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Q: A man 6 feet tall walks at a rate of 3 feet per second away from a light that is 15 feet above the…

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Q: If 14 g of a radioactive substance are present initially and 8 yr later only 7 g​ remain, how much…

A:

Q: A 50 mg sample of thorium-233 decays to 44 mg after 4 min. a) Determine the half-life of…

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Q: An element with mass 430 grams decays by 27.4% per minute. How much of the element is remaining…

A: We need to find the exponential function representing the decay of the element.

Q: . A small metal bar, whose initial temperature was 20° C, is dropped into a large container of…

A:

Q: A 50-mg sample of a radioactive substance decays to 34 mg after 30 days. How long will it take for…

A: The radioactive decay is modelled using the equation: N(t)=N0e-kt, where N0 is the initial amount…

Q: If 18g of a radioactive substance are present initially and 4 yr later only 9g​ remain, how many gs…

A: It is simple unitary method problem.

Q: Element X decays radioactively with a half life of 9 minutes. If there are 760 grams of Element X,…

A: Formula for half life is as below : N(t)=19 gramsN0=760t = ?t12=9 minutes

Q: The original quantity of a radioisotope was 100 mCi. How long will take to reduce to 75 mCi, if the…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.