A plaque assay is performed beginning with \(1.0 \mathrm{mL}\) of a solution containing bacteriophages. This solution is serially diluted three times by taking \(0.1 \mathrm{mL}\) and adding it to \(9.9 \mathrm{mL}\) of liquid medium. \(0.1 \mathrm{mL}\) of the final dilution is plated and yields 17 plaques. What is the initial density of bacteriophages in the original \(1.0 \mathrm{mL} ?\)

Short Answer

Expert verified
Answer: The initial density of bacteriophages in the original 1.0 mL solution is 170,000 plaques/mL.

Step by step solution

01

Find the dilution factor for each step

At each serial dilution, 0.1 mL is taken from the solution and added to 9.9 mL of liquid medium. The dilution factor is calculated as the total volume divided by the sample volume. In this case, the dilution factor for each step is \(\frac{9.9 + 0.1}{0.1} = 10\)
02

Calculate the total dilution factor

Since there are three serial dilutions, we need to multiply the dilution factor for each step together to find the total dilution factor: \(10 \times 10 \times 10 = 1000\)
03

Calculate the density of bacteriophages in the last dilution

We know that 0.1 mL of the last dilution yielded 17 plaques. To find the density of bacteriophages in the last dilution, we need to divide the number of plaques by the volume plated: \(\frac{17 \text{ plaques}}{0.1 \text{ mL}} = 170 \text{ plaques/mL}\)
04

Calculate the initial density of bacteriophages

To find the initial density of bacteriophages in the original 1.0 mL solution, we need to multiply the density of the last dilution by the total dilution factor: \(170 \text{ plaques/mL} \times 1000 = 170000 \text{ plaques/mL}\) So, the initial density of bacteriophages in the original \(1.0 \mathrm{mL}\) solution is \(170,000\) plaques/mL.

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