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Half Life

Akoranga 7 Mahi Tuatahi

  1. Date your book and collect a container of dice from the front
  2. Count the total number of dice
  3. Roll all the dice in one go. Set aside the dice with dots facing up, count the dice without dots and record that value.
  4. Roll all the dice in one go that did did not land with dots facing up. Discard those with dots facing up, count, record and repeat until no dice remain.
  5. Create a line graph showing the number of dice rolled (y-axis) vs the trial number (x-axis)

What you have graphed is an exponential decay curve! This is what nature does - we can observe it all over the place, even in electrical circuits.

It is not important to understand why at the moment, just to know that it does occur.


Mahi Tuatahi 2

  1. A Carbon-14 nucleus emits a beta particle, then the daughter nucleus also emits a beta particle immediately after. Write two equations to show this.
  2. An Uranium-241 nucleus emits an alpha particle AND a beta particle. Write down the equation.
  3. An atom of Carbon-11 absorbs a neutron. Write down the nuclear equation.

\begin{align*} {}^{14}_{6}C \rightarrow {}^{14}_{7}N + {}^{0}_{-1}\beta \newline {}^{14}_{7}N \rightarrow {}^{14}_{8}O + {}^{0}_{-1}\beta \end{align*}

\begin{align*} {}^{241}_{92}U \rightarrow {}^{237}_{87}Fr + {}^{4}_{2}\alpha + {}^{0}_{-1}\beta \end{align*}

\begin{align*} {}^{11}_{6}C + {}^{0}_{1}n \rightarrow {}^{12}_{6}C \end{align*}


Ngā Whāinga Ako

Write ngā whāinga ako in your books



Half-Life

The half-life is the time taken for half of the undecayed atoms in a sample to decay.


Tauira

A small sample of a radioactive material iodine-131 has been observed for several days while it decayed into xenon-131. Read the below and determine its half-life.


Iodide-131 Half-Life Graph


Pātai Tahi

The half-life of Hydrogen-3 is approximately 12.25 years. If you found a small sample of Tritium containing 5,000,000 undecayed nuclei.

  1. How many nuclei will be left after 12.25 years
  2. How many nuclei will be left after 24.5 years
  3. How many nuclei will be left after 49 years
  4. How many nuclei will be left after 196 years
  5. How long until there is less than 2500 undecayed nuclei left?

Whakatika Tahi

  1. 2,500,000
  2. 1,250,000
  3. 312,500
  4. 76.29
  5. Between 10-11 half-lives

Akoranga 8 Mahi Tuatahi

You found a $50 g$ sample of Cobalt-60. The half-life of Cobalt-60 is 5 years. What would be the mass of the Cobalt-60 sample after 20 years?

  1. Estimate how long it would take for the mass of the 50 g sample to fall just below $1.17 g$.
  2. Sketch a mass vs. time graph of the Cobalt-60 sample over a 30-year period.
  3. Use the graph to estimate the mass of the sample after 12.5 years.

Exponential Decay Curves

Source


Predictions

Source


Pātai: Predict time until 37.5% left

Source


Homework / Mahi Kāinga