Question

The half-life of Radon (which is a radioactive carcinogen) is 3.8 days. The safe level of Radon exposure is 400 Bq/m3. A house is found to be at a dangerous level of 8000 Bq/m3. If there is no input or output of the gas, will it be safe to enter the house in 16 days? 5. What is the Richter Scale measurement for an earthquake that is 5 times as intense as an earthquake measuring 8.2 on the Richter scale?

Answer 1

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

$\lambda=\dfrac{ln 2}{t_{\frac{1}{2}}}$

Put the value into the formula

$\lambda=\dfrac{ln 2}{3.8}$

$\lambda=0.182\ day^{-1}$

Now, $N =N_{0}e^{-\lambda t}$

Put the value into the formula

$N=8000\times e^{-0.182\times16}$

$N=434.93=435\ Bq/m^3$

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

$I_{1}=5I_{2}$....(I)

Using formula for Richter Scale measurement

We know that,

$M = log\dfrac{I}{5}$

For Earthquake of magnitude,

$M_{1}-M_{2}=log\dfrac{I_{1}}{5}-log\dfrac{I_{2}}{5}$

$M_{1}-M_{2}=log\dfrac{5I_{2}}{5}-log\dfrac{I_{2}}{5}$

$M_{1}-M_{2}=log(\dfrac{\dfrac{5I_{2}}{5}}{\dfrac{I_{2}}{5}})$

$M_{1}-M_{2}=log5$

$M_{1}=M_{2}+log5$

Put the value into the formula

$M_{1}=8.2+log 5$

$M_{1}=8.9$

Earthquake of magnitude 8.9 will be about 5 times as strong as earthquake of magnitude 8.2.

Hence, This is the required solution.