Respuesta :
Explanation:
Given that,
Time = 3.8 days
Radon exposure = 400 Bq/m³
Dangerous level = 8000 Bq/m³
Time = 16 days
We need to calculate the decay constant
Using formula of decay constant
[tex]\lambda=\dfrac{ln 2}{t_{\frac{1}{2}}}[/tex]
Put the value into the formula
[tex]\lambda=\dfrac{ln 2}{3.8}[/tex]
[tex]\lambda=0.182\ day^{-1}[/tex]
Now, [tex]N =N_{0}e^{-\lambda t}[/tex]
Put the value into the formula
[tex]N=8000\times e^{-0.182\times16}[/tex]
[tex]N=434.93=435\ Bq/m^3[/tex]
It is still not safe to enter the house after 16 days.
(B). We need to calculate the Richter Scale measurement for an earthquake
Given that,
Earthquake measurement = 8.2
[tex]I_{1}=5I_{2}[/tex]....(I)
Using formula for Richter Scale measurement
We know that,
[tex]M = log\dfrac{I}{5}[/tex]
For Earthquake of magnitude,
[tex]M_{1}-M_{2}=log\dfrac{I_{1}}{5}-log\dfrac{I_{2}}{5}[/tex]
[tex]M_{1}-M_{2}=log\dfrac{5I_{2}}{5}-log\dfrac{I_{2}}{5}[/tex]
[tex]M_{1}-M_{2}=log(\dfrac{\dfrac{5I_{2}}{5}}{\dfrac{I_{2}}{5}})[/tex]
[tex]M_{1}-M_{2}=log5[/tex]
[tex]M_{1}=M_{2}+log5[/tex]
Put the value into the formula
[tex]M_{1}=8.2+log 5[/tex]
[tex]M_{1}=8.9[/tex]
Earthquake of magnitude 8.9 will be about 5 times as strong as earthquake of magnitude 8.2.
Hence, This is the required solution.
