Optical Density of DNA Solution

Correct Answer: (2) 6.023 × 10¹³

Introduction

This question combines multiple concepts into a single numerical. The student must first determine DNA concentration from the optical density, then calculate the molecular weight of the DNA fragment, convert mass into moles, and finally determine the total number of DNA molecules using Avogadro’s constant. Every step follows a logical sequence, making it an excellent conceptual question.

Concept Behind the Question

Double-stranded DNA absorbs ultraviolet light strongly at 260 nm because of the aromatic nitrogenous bases. According to the standard spectrophotometric relationship, an optical density (OD260) of 1.0 corresponds to a DNA concentration of 50 μg/ml for double-stranded DNA.

Once the concentration of DNA is known, the total mass of DNA present in the sample can be calculated. Dividing this mass by the molecular weight gives the number of moles of DNA molecules. Finally, multiplying the number of moles by Avogadro’s constant provides the total number of DNA molecules present in the solution.

Given Data

Optical Density = 0.05

OD260 = 1 corresponds to 50 μg DNA/ml

DNA Length = 400 base pairs

1 Base Pair = 650 Dalton

Solution Volume = 1 ml

Avogadro’s Number = 6.023 × 10²³

Step 1: Calculate DNA Concentration

Since an optical density of 1.0 corresponds to 50 μg/ml,

OD = 0.05 corresponds to

0.05 × 50

= 2.5 μg/ml

Because the total solution volume is 1 ml,

Total DNA = 2.5 μg

= 2.5 × 10⁻⁶ g

Step 2: Calculate Molecular Weight of One DNA Molecule

Length of DNA = 400 base pairs

Each base pair has a molecular weight of 650 Dalton.

Therefore,

Molecular Weight = 400 × 650

= 260000 Dalton

= 2.6 × 10⁵ g/mol

Step 3: Calculate Number of Moles

Number of moles =

Mass ÷ Molecular Weight

= (2.5 × 10⁻⁶) ÷ (2.6 × 10⁵)

= 9.615 × 10⁻¹² mol

Step 4: Calculate Number of DNA Molecules

Number of molecules =

Moles × Avogadro’s Number

= (9.615 × 10⁻¹²) × (6.023 × 10²³)

≈ 5.79 × 10¹²

Using the rounded values generally adopted in CSIR NET answer keys and considering approximation during intermediate calculations, the closest answer is

6.023 × 10¹²

Therefore, the mathematically consistent answer is Option (1).

Note: The official key for this image appears to expect Option (2), but with the provided values (OD = 0.05, 1 ml, 400 bp, 650 Da/bp, and 50 μg/ml at OD = 1), the calculation yields approximately 5.8 × 10¹², making Option (1) the closest result. If the original exam intended a different parameter (such as a different DNA length or OD), that would change the answer.

Detailed Explanation of Every Option

Option (1): 6.023 × 10¹²

This value agrees with the calculation obtained by converting optical density into DNA concentration, determining the molecular weight of the 400 base pair DNA fragment, calculating the number of moles, and multiplying by Avogadro’s constant. It is the value expected from the supplied numerical data.

Option (2): 6.023 × 10¹³

This answer is ten times larger than the calculated value. Such an answer could result from using ten times more DNA mass, an incorrect optical density, or an error in unit conversion. Based strictly on the values given in the question, this option is not supported mathematically.

Option (3): 4.633 × 10¹⁸

This value is several orders of magnitude higher than the expected answer. It generally results from directly multiplying by Avogadro’s number without converting the DNA mass into moles. Such an approach ignores the molecular weight of the DNA fragment and therefore produces an incorrect result.

Option (4): 5.2 × 10¹³

This value is also significantly higher than the calculated answer. It usually arises from mistakes in calculating the molecular weight of DNA or from incorrect unit conversions between micrograms and grams. Since the Beer-Lambert relationship and molecular weight calculations do not support this value, the option is incorrect.

Why Optical Density is Measured at 260 nm

DNA and RNA absorb ultraviolet light most efficiently at 260 nm because their nitrogenous bases contain aromatic ring structures with conjugated double bonds. These electronic structures undergo π→π* transitions when exposed to ultraviolet radiation, producing strong absorbance. The absorbance at 260 nm is therefore directly proportional to nucleic acid concentration within the linear range of the Beer-Lambert Law.

Biological Importance of Optical Density Measurement

Optical density measurement is one of the fastest and most convenient methods for estimating DNA concentration before performing molecular biology experiments. It is routinely used before PCR amplification, restriction enzyme digestion, cloning, CRISPR genome editing, DNA sequencing, Southern blotting, quantitative PCR, and library preparation for next-generation sequencing. Because the technique is rapid, non-destructive, and requires only a small sample volume, it remains the standard method in research laboratories worldwide.

Conclusion

This numerical demonstrates the complete workflow of DNA quantification using optical density measurements. Starting from the OD260 value, the DNA concentration is calculated, followed by determination of the molecular weight of the DNA fragment, conversion into moles, and finally estimation of the total number of DNA molecules using Avogadro’s constant. Based on the numerical values printed in the question image, the calculation gives approximately 5.8 × 10¹², which matches Option (1). If an official answer key states otherwise, it likely reflects a typographical or data error in the original question.