Each element has a characteristic atomic mass. The atoms are extremely small particles and it is very difficult to determine their actual masses. For example, mass of one atom of hydrogen has been found to be `1.66 xx 10^(-24)` . Obviously, such a small mass cannot be determined even with the help of a very sensitive balance. To overcome, this problem, the atomic masses are expressed as relative masses i.e., with reference to mass of a standard atom. In 1961, the International Union of Chemists selected the stable isotope of carbon ( carbon -12) as the standard for comparing the atomic and molecular masses of elements and compounds. The atomic mass of the standard, the isotope carbon-12 of carbon is chosen to be 12. Thus, atomic mass may be defined as the relative mass of an atom of the element as compared to an atom of carbon ( carbon-12) taken as 12.
Arrange the following in the increasing order of mass in grams `:`
(I) One atom of silver
(II) Two grams atom of nitrogen
(III) One mole of calcium
(IV) Two grams of sodium
[ At. masses `:` Ag = 108u, N = 14u, C a= 40 u, Na =23u]

Options

A. `I lt II lt III lt IV`
B. `IV lt III lt II lt I`
C. `I lt IV lt II lt III`
D. `III lt II lt I lt IV`

Explanation

To solve the problem of arranging the given items in increasing order of mass in grams, we will first calculate the mass of each item based on the provided atomic masses.

### Step 1: Calculate the mass of one atom of silver
- The atomic mass of silver (Ag) is given as 108 u.
- The mass of one atom of silver in grams can be calculated using the formula:
\[ \text{Mass of one atom} = \frac{\text{Atomic mass (in grams per mole)}}{N_A} \]
where \( N_A \) (Avogadro's number) is approximately \( 6.02 \times 10^{23} \).

\[ \text{Mass of one atom of Ag} = \frac{108 \text{ g/mol}}{6.02 \times 10^{23}} \approx 1.79 \times 10^{-22} \text{ g} \]

### Step 2: Calculate the mass of two grams of nitrogen
- The atomic mass of nitrogen (N) is given as 14 u.
- Since we are given 2 grams of nitrogen, we can directly use this value.

\[ \text{Mass of 2 grams of N} = 2 \text{ g} \]

### Step 3: Calculate the mass of one mole of calcium
- The atomic mass of calcium (Ca) is given as 40 u.
- One mole of calcium weighs exactly its atomic mass in grams.

\[ \text{Mass of 1 mole of Ca} = 40 \text{ g} \]

### Step 4: Calculate the mass of two grams of sodium
- The atomic mass of sodium (Na) is given as 23 u.
- Similar to nitrogen, we are given 2 grams of sodium, which we can directly use.

\[ \text{Mass of 2 grams of Na} = 2 \text{ g} \]

### Step 5: Summarize the masses calculated
1. One atom of silver: \( 1.79 \times 10^{-22} \text{ g} \)
2. Two grams of nitrogen: \( 2 \text{ g} \)
3. One mole of calcium: \( 40 \text{ g} \)
4. Two grams of sodium: \( 2 \text{ g} \)

### Step 6: Arrange the masses in increasing order
- The mass of one atom of silver is significantly smaller than the other values.
- Both two grams of nitrogen and two grams of sodium are equal, but they are greater than the mass of one atom of silver.
- The mass of one mole of calcium is the largest.

Thus, the increasing order of mass in grams is:
1. One atom of silver: \( 1.79 \times 10^{-22} \text{ g} \)
2. Two grams of nitrogen: \( 2 \text{ g} \)
3. Two grams of sodium: \( 2 \text{ g} \)
4. One mole of calcium: \( 40 \text{ g} \)

### Final Arrangement:
- One atom of silver < Two grams of nitrogen = Two grams of sodium < One mole of calcium