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
Grace [21]
3 years ago
12

Two different radioactive isotopes decay to 10% of their respective original amounts. Isotope A does this in 33 days, while isot

ope B does this in 43 days. What is the approximate difference in the half-lives of the isotopes?
Mathematics
2 answers:
Maslowich3 years ago
6 0

Answer:

A. 3 Days

Step-by-step explanation:

Just took the test hope this helps :)

Andrews [41]3 years ago
4 0

Answer:

The approximate difference in the half-lives of the isotopes is 66 days.

Step-by-step explanation:

The decay of an isotope is represented by the following differential equation:

\frac{dm}{dt} = -\frac{t}{\tau}

Where:

m - Current mass of the isotope, measured in kilograms.

t - Time, measured in days.

\tau - Time constant, measured in days.

The solution of the differential equation is:

m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }

Where m_{o} is the initial mass of the isotope, measure in kilograms.

Now, the time constant is cleared:

\ln \frac{m(t)}{m_{o}} = -\frac{t}{\tau}

\tau = -\frac{t}{\ln \frac{m(t)}{m_{o}} }

The half-life of a isotope (t_{1/2}) as a function of time constant is:

t_{1/2} = \tau \cdot \ln2

t_{1/2} = -\left(\frac{t}{\ln\frac{m(t)}{m_{o}} }\right) \cdot \ln 2

The half-life difference between isotope B and isotope A is:

\Delta t_{1/2} = \left| -\left(\frac{t_{A}}{\ln \frac{m_{A}(t)}{m_{o,A}} } \right)\cdot \ln 2+\left(\frac{t_{B}}{\ln \frac{m_{B}(t)}{m_{o,B}} } \right)\cdot \ln 2\right|

If \frac{m_{A}(t)}{m_{o,A}} = \frac{m_{B}(t)}{m_{o,B}} = 0.9, t_{A} = 33\,days and t_{B} = 43\,days, the difference in the half-lives of the isotopes is:

\Delta t_{1/2} = \left|-\left(\frac{33\,days}{\ln 0.90} \right)\cdot \ln 2 + \left(\frac{43\,days}{\ln 0.90} \right)\cdot \ln 2\right|

\Delta t_{1/2} \approx 65.788\,days

The approximate difference in the half-lives of the isotopes is 66 days.

You might be interested in
Help pleasee don’t know what I’m doing lol
Ksju [112]

Answer:

D. 4\sqrt{3} in

Step-by-step explanation:

Hope this helps!

7 0
3 years ago
Read 2 more answers
A parallelogram cannot be a cross section of a triangular prism
abruzzese [7]
The question presented is not answerable because it just presented a mere statement. 
7 0
3 years ago
Read 2 more answers
What is 936,292 rounded to the nearest hundred thousand
Romashka [77]
The answer is 900,000?
3 0
3 years ago
Enter the correct number word to complete the conversion. 1 milliampere = one ? of an ampere
Lerok [7]

Answer:

One milliampere is equal to 0.001 ampere.

Step-by-step explanation:

Mili, refers to thousandth. (for example, millimeter or milliliter.)

6 0
3 years ago
47/7 as a mixed number in siplest form
puteri [66]
For this fraction, you would have to see how many times 7 goes into 47. So, 6 times as 7 times 6 is 42. Subtract 42 from 47, and this would be your remainder:

6\frac{5}{7} 
7 0
3 years ago
Read 2 more answers
Other questions:
  • If the value of 2x3 is 2, then what is the value of x?
    8·1 answer
  • Algebra 2 please help
    12·1 answer
  • Say a friend had multiplied 1.2 and 2.6 and got 31.2. would that be the correct answer
    14·1 answer
  • Merideth's brother, Miles, is 3 years younger than twice her age. The sum of their ages is 24. Create an equation to determine t
    14·1 answer
  • Solve for y in terms of x: 3y-2x=7
    13·2 answers
  • 11. A video receives 10,678 views the first day. It receives
    10·1 answer
  • Which dimensions cannot create a triangle?
    13·1 answer
  • 1. A pyramid with a square base has fixed volume. The height, t, varies inversely as the
    14·1 answer
  • An astronaut who weighs 95 kilograms on Earth weighs 15.8 kilograms on the Moon. How much would a person weigh on the Moon if th
    14·1 answer
  • Help
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!