Question

220 In an experiment with the radioactive isotope Rn86 of radon gas, Ruther- ford made the following measurements of the quotient $\frac{y'(t)}{y'(0)}$ of the de- cay rates for the specimen he was studying: in $t = 40s$, $\frac{y'(t)}{y'(0)} = 0,60$; in t = 80 s, $\frac{y'(t)}{y'(0)} = 0,36$ in t = 120 s, $\frac{y'(t)}{y'(0)} = 0,22$. a) Draw the graph of the points $(0, 0)$, $(40, ln(0,60))$, $(80, ln(0,36))$, $(120, ln(0,222))$ en $R^2$. These four points can be approximated to a line $-\lambda$, what is the value of lambda $\lambda$? This $\lambda$ is called the decay or decay constant of the element. b) Find the function $y(t)$, which is the number of atoms at a time t. c) The half-life of a radioactive element is the time it takes for the spe- cimen to decay to half its initial size. What is the half-life of $Rn_{86}^{220}$ ? d) What fraction of the initial number of atoms $y_0$ that remained after 5 minutes? e) Assuming that $y_0 = y(0) = 10^9$, How many atoms disintegrated in 2 seconds? What was the average rate of disintegration per second over these two seconds? What was the rate of decay per second at t = 2 s?

          220
In an experiment with the radioactive isotope Rn86 of radon gas, Ruther-
ford made the following measurements of the quotient $\frac{y'(t)}{y'(0)}$ of the de-
cay rates for the specimen he was studying: in $t = 40s$, $\frac{y'(t)}{y'(0)} = 0,60$; in
t = 80 s, $\frac{y'(t)}{y'(0)} = 0,36$ in t = 120 s, $\frac{y'(t)}{y'(0)} = 0,22$.
a) Draw the graph of the points $(0, 0)$, $(40, ln(0,60))$, $(80, ln(0,36))$, $(120, ln(0,222))$
en $R^2$. These four points can be approximated to a line $-\lambda$, what is the
value of lambda $\lambda$? This $\lambda$ is called the decay or decay constant of the
element.
b) Find the function $y(t)$, which is the number of atoms at a time t.
c) The half-life of a radioactive element is the time it takes for the spe-
cimen to decay to half its initial size. What is the half-life of $Rn_{86}^{220}$ ? d)
What fraction of the initial number of atoms $y_0$ that remained after 5
minutes?
e) Assuming that $y_0 = y(0) = 10^9$, How many atoms disintegrated in
2 seconds? What was the average rate of disintegration per second over
these two seconds? What was the rate of decay per second at t = 2 s?

$220 In an experiment with the radioactive isotope Rn86 of radon gas, Ruther- ford made the following measurements of the quotient (y'(t))/(y'(0)) of the de- cay rates for the specimen he was studying: in t = 40s, (y'(t))/(y'(0)) = 0,60; in t = 80 s, (y'(t))/(y'(0)) = 0,36 in t = 120 s, (y'(t))/(y'(0)) = 0,22. a) Draw the graph of the points (0, 0), (40, ln(0,60)), (80, ln(0,36)), (120, ln(0,222)) en R^2. These four points can be approximated to a line -λ, what is the value of lambda λ? This λ is called the decay or decay constant of the element. b) Find the function y(t), which is the number of atoms at a time t. c) The half-life of a radioactive element is the time it takes for the spe- cimen to decay to half its initial size. What is the half-life of Rn86^220 ? d) What fraction of the initial number of atoms y0 that remained after 5 minutes? e) Assuming that y0 = y(0) = 10^9, How many atoms disintegrated in 2 seconds? What was the average rate of disintegration per second over these two seconds? What was the rate of decay per second at t = 2 s?$

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