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
Oxana [17]
3 years ago
12

The initial activity of 37Ar is 8540 disintegrations per minute. After 10.0 days, the activity is 6990 disintegrations per minut

e. what is the activity after 47.2 days?​
Chemistry
1 answer:
mylen [45]3 years ago
8 0

Answer:

Approximately 3318 disintegrations per minute.

Explanation:

The activity A of a radioactive decay at time t can be found with the following equation:

\displaystyle A(t) = A_0 \cdot \mathrm{e}^{-\lambda\cdot t}.

In this equation,

  • \mathrm{e} is the natural base. \mathrm{e}\approx 2.71828.
  • A_0 is the initial activity of the decay. For this question, A_0 = \rm 8540\; min^{-1}.
  • The decay constant \lambda of this sample needs to be found.

The decay constant here can be found using the activity after 10 days. As long as both times are in the same unit (days in this case,) conversion will not be necessary.

A(10) = A_0\cdot \mathrm{e}^{\rm -\lambda \times 10\;day}= (\mathrm{8540\; min^{-1}})\cdot \mathrm{e}^{\rm -\lambda \times 10\;day}.

A(10) = \rm 6690\; min^{-1}.

\displaystyle \frac{\rm 6690\; min^{-1}}{\mathrm{8540\; min^{-1}}} = \mathrm{e}^{\rm -\lambda \times 10\;day}

Apply the natural logarithm to both sides of this equation.

\displaystyle \ln{\left(\frac{\rm 6690\; min^{-1}}{\mathrm{8540\; min^{-1}}}\right)} = \ln{\left(\mathrm{e}^{\rm -\lambda \times 10\;day}\right)}.

\displaystyle \rm -\lambda \cdot (10\;day) = \ln{\left(\frac{\rm 6690\; min^{-1}}{\mathrm{8540\; min^{-1}}}\right)}.

\displaystyle \rm \lambda= \rm \frac{\displaystyle \ln{\left(\frac{\rm 6690\; min^{-1}}{\mathrm{8540\; min^{-1}}}\right)}}{-10 \; day} \approx 0.0200280\; day^{-1}.

Note that the unit of the decay constant \lambda is \rm day^{-1} (the reciprocal of days.) The exponent -\lambda \cdot t should be dimensionless. In other words, the unit of t should also be days. This observation confirms that there's no need for unit conversion as long as the two times are in the same unit.

Apply the equation for decay activity at time t to find the decay activity after 47.2 days.

\displaystyle \begin{aligned}A(t)& = A_0 \cdot \mathrm{e}^{-\lambda\cdot t}\\&\approx \rm \left(8540\; min^{-1}\right)\cdot \mathrm{e}^{-0.0200280\; day^{-1}\times 47.2\;day}\\&\approx \rm 3318\; min^{-1}\end{aligned}.

By dimensional analysis, the unit of activity here should also be disintegrations per minute. The activity after 47.2 days will be approximately 3318 disintegrations per minute.

You might be interested in
What is the chemical formula for the binary compound nitrogen dioxide?
-Dominant- [34]
NO2 Hope this helped!
4 0
3 years ago
Read 2 more answers
Consider a solution containing .100 M fluoride ions and .126M hydrogen fluoride. The concentration of fluoride ions after the ad
S_A_V [24]
Given:

Concentration of Fluoride ions = 0.100 M
Concentration of Hydrogen Fluoride = 0.126 M

Asked: Concentration of fluoride ions after the addition of 5ml of 0.0100 M HCl to 25 mL of the solution

Assume: 50:50 ratio of fluoride ions and HF

12.5ml*0.1mol/L *1L/1000mL + 12.5*0.126mol/L * 1L/1000mL = 2.825x10^-3 moles F-

5ml * 0.01 mol/L *1L/1000mL = 5x10^-5 moles

Assume: Volume additive

Final concentration = 2.825x10^-3 + 5x10^-5 moles/ 30 ml * 1000ml/L =0.0958 M
<span />
3 0
3 years ago
How many dozen (dz) eggs are needed to make 12 muffins? What about 15.5
NARA [144]

Answer:

I think its 1.2 cause I divided 15.5 with 12 and got 1.2 as an answer

8 0
3 years ago
Read 2 more answers
What is the atomic number of this atom?
PIT_PIT [208]

Answer:

2?????

Explanation:

6 0
3 years ago
Read 2 more answers
Which sample of water contains particles having the highest average kinetic energy ?
creativ13 [48]
25mL if water as the highest average of the kinetic energy
3 0
3 years ago
Other questions:
  • Which of the following groups of carbon compounds includes enzymes? lipids proteins carbohydrates nucleic acids
    14·1 answer
  • What kind of charge does a cation have
    11·2 answers
  • A 3.82-g sample of magnesium nitride is reacted with 7.73 g of water. mg3n2 (s) + 3 h2o (â) â 2 nh3 (g) + 3 mgo (s) the yield of
    11·1 answer
  • Why would it be more difficult to inject the nucleus of uranium with a proton?
    6·1 answer
  • Select all that apply to physical and chemical properties ?
    9·2 answers
  • How many grams of sucrose, molecular mass 342.34 g/mol, are dissolved in water to make 500. ml of a 0.462 m solution?
    8·1 answer
  • A piston-cylinder device initially contains water liquid-vapor mixture at the pressure of 700 kPa. The liquid-vapor mixture has
    9·1 answer
  • How to calculate the mass percent of hydrogen
    10·1 answer
  • Post-Lecture Assignment Chapter 06
    7·1 answer
  • Which quantity must be determined experimentally in order to determine the bonding atomic radius of an atom?.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!