Answer :
In Tube 3's dilution, 1 to 625 arises from successive 1 to 2 dilutions in four tubes during a five fold serial dilution, hence the correct option is C. 1 to 625.
Let's break down the dilution process step by step:
Tube 1: Initially, we have a [tex]\(1:2\)[/tex] dilution, meaning for every 1 part of the original substance, we add 2 parts of diluent. So, the dilution factor for Tube 1 is [tex]\(1:2\)[/tex].
Tube 2: To calculate the dilution factor for Tube 2, we take the dilution factor of Tube 1 and multiply it by itself, since the same dilution is repeated. Therefore, [tex]\(1:2 \times 1:2 = 2:1\)[/tex]. This means for every 2 parts of the diluted solution from Tube 1, we add 1 part of diluent.
Tube 3: Similarly, for Tube 3, we take the dilution factor of Tube 2 [tex](\(2:1\))[/tex] and multiply it by the dilution factor of Tube 1 [tex](\(1:2\))[/tex]. This gives us [tex]\(2:1 \times 1:2 = 4:1\)[/tex]. So, for every 4 parts of the diluted solution from Tube 2, we add 1 part of diluent.
Tube 4: Finally, for Tube 4, we repeat the process. The dilution factor of Tube 3 [tex](\(4:1\))[/tex] is multiplied by the dilution factor of Tube 1 [tex](\(1:2\))[/tex], resulting in [tex]\(4:1 \times 1:2 = 8:1\)[/tex]. This means for every 8 parts of the diluted solution from Tube 3, we add 1 part of diluent.
Therefore, the dilution in Tube 3 is [tex]\(8:1\)[/tex], which corresponds to option C. 1 to 625.
