Half-life

Half life with a spreadsheet

In this activity you will create a simulation of radioactive decay using a spreadsheet.

1. Top Rows Set-up:

   1. Cell B1: Decay Probability

   2. Cell C1: Whole number between 1 and 10

      1. This sets the probability of a nucleus decaying. If the number is high there is more chance of a nucleus decaying, if the number is low there is less chance of a nucleus decaying.

   3. Cell D1: Decay

   4. Cell D2: Remaining

   5. Cells E1 -> Q1: Number 1->12

   6. Cells E2 -> Q2: Set equal to remaining unstable nuclei per decay

2. Isotope Decay Model:

   1. ROW 6: Heading of Decay Model

      1. A6: # of Atom

      2. B6: Decay 1

      3. C6: =sum(c7:c106) This will count the number of remaining unstable nuclei.

      4. D6 ->Y6: Repeat B6 and C6 info making appropriate changes.

3. Rows 7 -> 106 (100 rows = 100 atoms)

   1. A7: =Row()-6

      1. This sets the value of the cell to the row number minus the starting point, it should return a value of 1

   2. B7: =RandBetween(1,10)

      1. This is a random number generator and in this case will generate a number between 1 and 10.

   3. C7: =if(B7<$C$1,0,1) ((=if(Condition,THEN,ELSE)

      1. This reads as follows: If B7 is less than C1, then return '0', else return '1'.

      2. This means that if the number in column B is less your decay probability number in C1 (in this case 6) then a 0 is registered - this represents a nucleus that has decayed. If the number in column B is equal to or more than 6, then a 1 is registered - this represents a nucleus that has not decayed. The dollar signs ($) lock the formula to the cell C1.

   4. D7: =if(C7=1,RandBetween(1,10),0)

      2. 1. This reads as follows: If C7 equals 1 then produce a random number between 1 and 10, if C7 does not equal 1 the produce a 0 (also read as else 0).

   5. E7->Y7: Repeat of C7:D7

      1. You should be able to copy C7:D7 into each of the columns.

   6. Once you have ROW 7 setup, select all the cells and drag the contents to ROW 106 using the small blue box in the lower right hand corner.

   7. You should now have a large array of data that changes when you change a cell.

4. Add analysis and visuals:

   1. C6: =sum(C7:c106)

      1. This will return a total of unstable nuclei.

      2. You will use this value in your data table in D1:Q2

   2. Conditional Formatting:

      1. Using the FORMAT... Conditional Formatting... tool, set a rule so that unstable nuclei (cell value = 1) are green

1. Create a Graph:

   1. Using the data in D1:Q2, create a Scatter Plot of your data.

   2. Add an EXPONENTIAL trendline, labeled with the equation.

2. Produce continuous new sets of data:

   1. FILE...SPREADSHEET SETTINGS...CALCULATIONS

   2. Set RECALCULATION to "On change and every minute"