Respuesta :
Using an exponential equation, it is found that:
- [tex]3.9144 \times 10^{18}[/tex] atoms would disintegrate in 1 hour and 45 minutes.
- 0.0313 = 3.13% of the original sample remains.
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An exponential equation for the proportion of a substance after m minutes is given by:
[tex]P(m) = e^{-km}[/tex]
- In which k is the decay rate.
The half-life of francium is 21 minutes.
This means that:
[tex]P(21) = 0.5[/tex]
This is used to find k.
[tex]e^{-21k} = 0.5[/tex]
[tex]\ln{e^{-21k}} = \ln{0.5}[/tex]
[tex]-21k = \ln{0.5}[/tex]
[tex]k = -\frac{\ln{0.5}}{21}[/tex]
[tex]k = 0.033[/tex]
Thus
[tex]P(m) = e^{-0.033m}[/tex]
After 1 hour and 45 minutes:
- 105 minutes, thus, the fraction for the proportion that remains is P(105).
[tex]P(105) = e^{-0.033(105)} = 0.0313[/tex]
0.0313 = 3.13% of the original sample remains.
- Initially, there was [tex]4 \times 10^{18}[/tex] atoms.
- 0.0313 remained, so 1 - 0.0313 = 0.9687 disintegrated.
The number of atoms that disintegrated is:
[tex]0.9687 \times 4 \times 10^18 = 3.9144 \times 10^{18}[/tex]
[tex]3.9144 \times 10^{18}[/tex] atoms would disintegrate in 1 hour and 45 minutes.
A similar problem is given at https://brainly.com/question/23416643
