The protonic charge in \(100 \mathrm{gm}\) of water is $\ldots \ldots . . \mathrm{c}$ (A) \(4.8 \times 10^{5}\) (B) \(5.4 \times 10^{6}\) (C) \(3.6 \times 10^{4}\) (D) \(4.9 \times 10^{6}\)

First, we need to determine the number of moles of water in the given 100 g sample. To find the moles, we will use the formula: Moles = Mass / Molar mass The molar mass of water (H₂O) is the sum of the atomic masses of two hydrogen atoms (each 1 g/mol) and one oxygen atom (16 g/mol): Molar mass of water = 2 * 1 + 16 = 18 g/mol. Now we can calculate the moles of water in the sample: Moles of water = \( \frac{100 \text{ g}}{18 \text{ g/mol}} \) = 5.56 moles (rounded to two decimal places).

Next, we will find the number of protons in the 5.56 moles of water. Water has 10 protons per molecule: 8 protons from the oxygen atom and 1 proton from each of the two hydrogen atoms. To find the total number of water molecules in the sample, we will use the formula: Number of molecules = Moles × Avogadro's number Avogadro's number is \( 6.022 \times 10^{23} \) molecules/mol. Number of water molecules = 5.56 moles × \( 6.022 \times 10^{23} \) molecules/mol = \( 3.348 \times 10^{24} \) molecules Now, we can find the total number of protons in the sample by multiplying the number of water molecules by the number of protons per water molecule: Total number of protons = \( (3.348 \times 10^{24} \) water molecules) x (10 protons/water molecule) = \(3.348 \times 10^{25} \) protons

Finally, we will calculate the protonic charge using the total number of protons in the sample. The charge of a single proton is approximately \( 1.6 \times 10^{-19} \) C (Coulombs). To find the total protonic charge, we will multiply the charge of a single proton by the total number of protons: Protonic charge = \( (1.6 \times 10^{-19} \text{ C/proton}) \times (3.348 \times 10^{25} \text{ protons}) = 5.3568 \times 10^{6} \text{ C} \) Comparing with the given options, we can round the protonic charge to \( 5.4 \times 10^{6} \) C. Therefore, the correct answer is (B) \( 5.4 \times 10^{6} \) C.