Question

Recall that your hypothesis is that these values are the fraction of atoms that are still radioactive after n half-life cycles. Record in the appropriate blanks.

Answer 1

$0.5^{n}$ means 0.5 raise to the power of n. "To the power of" means an action of multiplication of 0.5 to n times.

The different values of n are given in the table. Substituting these values:

For A:

n = 1 (given)

$0.5^{n} = 0.5^{1} = 0.5$

For B:

n = 2 (given)

$0.5^{n} = 0.5^{2} = 0.5\times 0.5 = 0.25$

For C:

n = 3 (given)

$0.5^{n} = 0.5^{3} = 0.5\times 0.5\times 0.5 = 0.125$

For D:

n = 6 (given)

$0.5^{n} = 0.5^{6} = 0.5\times 0.5\times 0.5\times 0.5\times 0.5\times 0.5= 0.015625$

For E:

n = 8 (given)

$0.5^{n} = 0.5^{8} = 0.5\times 0.5\times 0.5\times 0.5\times 0.5\times 0.5\times 0.5\times 0.5= 0.00390625$

Hence, the values are:

A = 0.5

B = 0.25

C = 0.125

D = 0.015625

E = 0.00390625

Answer 2

A= 0.5
B= 0.25
C= 0.125
D= 0.015625
E= 0.00390625