The answer is A.

Weight of Nitrogen in a compound is equal to 28.9% of 194 i.e. (28.9/100) × 194So no. of N atoms are 28.9×194/14×100 = 4

The molecular weight of a compound is the sum of the atomic weights of all the atoms in its chemical formula. To determine the number of atoms of nitrogen in one molecule of caffeine, we need to calculate the molecular formula of caffeine and identify the number of nitrogen atoms.

Calculating the Molecular Formula of Caffeine:
1. Given that the molecular weight of caffeine is 194, we know that the sum of the atomic weights of all the atoms in one molecule of caffeine is 194.
2. The atomic weight of nitrogen is 14, so we need to determine the percentage of nitrogen in caffeine to calculate the number of nitrogen atoms.
3. Given that caffeine contains 28.9% nitrogen by mass, we can calculate the mass of nitrogen in one molecule of caffeine using the formula:

Mass of nitrogen = (Percentage of nitrogen by mass / 100) * Molecular weight of caffeine

Mass of nitrogen = (28.9 / 100) * 194 = 56.146 g/mol

Determining the Number of Nitrogen Atoms:
4. The atomic weight of nitrogen is 14 g/mol, so we can calculate the number of nitrogen atoms in one molecule of caffeine using the formula:

Number of nitrogen atoms = Mass of nitrogen / Atomic weight of nitrogen

Number of nitrogen atoms = 56.146 g/mol / 14 g/mol = 4

Therefore, the number of atoms of nitrogen in one molecule of caffeine is 4.

Summary:
- The molecular weight of caffeine is 194 and it contains 28.9% nitrogen by mass.
- By calculating the mass of nitrogen, we find that it is 56.146 g/mol.
- Dividing the mass of nitrogen by the atomic weight of nitrogen, we determine that there are 4 atoms of nitrogen in one molecule of caffeine.