1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
SSSSS [86.1K]
3 years ago
6

The barium isotope 133Ba has a half-life of 10.5 years. A sample begins with 1.1×1010 133Ba atoms. How many are left after (a) 6

years, (b) 10 years, and (c) 200 years?
Chemistry
1 answer:
Svetach [21]3 years ago
6 0

Answer:

(a) 7.4 x 10⁹ atoms.

(b)

(c)

Explanation:

  • It is known that the decay of a radioactive isotope isotope obeys first order kinetics.
  • Half-life time is the time needed for the reactants to be in its half concentration.
  • If reactant has initial concentration [A₀], after half-life time its concentration will be ([A₀]/2).
  • Also, it is clear that in first order decay the half-life time is independent of the initial concentration.
  • The half-life of 133-Ba = 10.5 years.

  • For, first order reactions:

<em>k = ln(2)/(t1/2) = 0.693/(t1/2).</em>

Where, k is the rate constant of the reaction.

t1/2 is the half-life of the reaction.

∴ k =0.693/(t1/2) = 0.693/(10.5 years) = 0.066 year⁻¹.

  • Also, we have the integral law of first order reaction:

kt = ln([A₀]/[A]),

where, k is the rate constant of the reaction (k = 0.066 year⁻¹).

t is the time of the reaction.

[A₀] is the initial concentration of (133-Ba) ([A₀] = 1.1 x 10¹⁰ atoms).

[A] is the remaining concentration of (133-Ba) ([A] = ??? g).

<u><em>(a) 6 years:</em></u>

t = 6.0 years.

∵ kt = ln([A₀]/[A])

∴ (0.066 year⁻¹)(6.0 year) = ln((1.1 x 10¹⁰ atoms)/[A])

∴ 0.396 = ln((1.1 x 10¹⁰ atoms)/[A]).

<em>Taking exponential for both sides:</em>

∴ 1.486 = ((1.1 x 10¹⁰ atoms)/[A]).

∴ [A] = (1.1 x 10¹⁰ atoms)/(1.486) = 7.4 x 10⁹ atoms.

<u><em>(b) 10 years</em></u>

t = 10.0 years.:

∵ kt = ln([A₀]/[A])

∴ (0.066 year⁻¹)(10.0 year) = ln((1.1 x 10¹⁰ atoms)/[A])

∴ 0.66 = ln((1.1 x 10¹⁰ atoms)/[A]).

<em>Taking exponential for both sides:</em>

∴ 1.935 = ((1.1 x 10¹⁰ atoms)/[A]).

∴ [A] = (1.1 x 10¹⁰ atoms)/(1.935) = 5.685 x 10⁹ atoms.

<u><em>(c) 200 years:</em></u>

t = 200.0 years.

∵ kt = ln([A₀]/[A])

∴ (0.066 year⁻¹)(200.0 year) = ln((1.1 x 10¹⁰ atoms)/[A])

∴ 13.2 = ln((1.1 x 10¹⁰ atoms)/[A]).

<em>Taking exponential for both sides:</em>

∴ 5.4 x 10⁵ = ((1.1 x 10¹⁰ atoms)/[A]).

∴ [A] = (1.1 x 10¹⁰ atoms)/(5.4 x 10⁵) = 2.035 x 10⁴ atoms.

You might be interested in
Using the periodic table and your knowledge of atomic structure. Would Carbon-14 have more, less or the same number of neutrons
Brilliant_brown [7]
D) <span> It has more neutrons. Its mass number is larger than the atomic mass number for carbon. </span>
4 0
3 years ago
Read 2 more answers
In which two types of reactions do opposite chemical changes occur
RideAnS [48]

Hello!

Before I can answer your question we need to know the different types of chemical reactions that can occur:

  • Single Replacement
  • Double Replacement
  • Synthesis
  • Decomposition
  • Combustion

Combustion is an answer that can usually be ruled out unless oxidation is occuring in the chemical equation (hyrdrogen occuring with oxygen to react)

Synthesis reaction, also known as a Combination reaction, is when the reactants combine to form a single product.

Decompostion is when a single reactant is deconstructed to form multiple products, or the opposite of Synthesis.


With these definitions alone, since they are opposite types of reactions, the answer would be Synthesis and Decomposition reactions !

Hope this helps and if you need anymore clarification feel free to ask.


4 0
3 years ago
Which of the following statements is most accurate?
Troyanec [42]

Answer:

B

Explanation:

This is because exothermic reactions occurs when bnds are formed, and involves the release of energy.

Endothermic reaction occur when bonds are broken,and involves absorption of energy.

4 0
3 years ago
Two angles with measures (6x + 60) (90)<br> are supplementary. What is the value of x?
fredd [130]
Supplementary angles add up to 180, so
6x+60+90 = 180 and solve for x
6x= 30
x=5
5 0
3 years ago
Read 2 more answers
Bronze is an alloy, which is what form of matter?
grandymaker [24]
It is a Compound. have a nice day
3 0
3 years ago
Read 2 more answers
Other questions:
  • What is the voltage of a cell with half-reactions Zn(s) = Zn2+ + 2e-
    12·1 answer
  • How do you know which element is the most reactive in the periodic table?
    5·1 answer
  • At constant pressure, how are the temperature and volume of a gas related?
    10·2 answers
  • Which word equation shows hydrogen reacting with oxygen to form water?
    6·1 answer
  • The value of the atomic mass of an atom is?<br><br> please help!!
    10·2 answers
  • In volumetric analysis, how does one convert concentration from g/dm3 to mol/dm3?
    10·1 answer
  • Put these atoms in order from most negative overall charge to least negative
    10·1 answer
  • A coffee cup has a heat capacity of 62.6 - If the coffee cup's temperature increases by 1.20°C, how much heat has it
    5·1 answer
  • Why is a neutral solution neutral?
    15·2 answers
  • Since gasses weigh nothing when they are produced in a reaction they do not have to be accounted for.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!