Arrange the following in the order of increasing mass (atomic mass: O=16, Cu-63, N-14)
I. one atom of oxygen
II. one atom of nitrogen
III `1 xx 10^(-10)` mole of oxygen
IV. `1 xx 10^(-10)` mole of copper

Options

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

Explanation

To solve the problem of arranging the given options in the order of increasing mass, we will calculate the mass of each option step by step.

### Given Data:
- Atomic mass of Oxygen (O) = 16 g/mol
- Atomic mass of Nitrogen (N) = 14 g/mol
- Atomic mass of Copper (Cu) = 63 g/mol
- 1 mole = \(6.022 \times 10^{23}\) atoms

### Step 1: Calculate the mass of one atom of Oxygen (Option I)
- The mass of one atom of Oxygen:
\[ \text{Mass of 1 atom of O} = \frac{16 \text{ g}}{6.022 \times 10^{23}} \approx 2.66 \times 10^{-23} \text{ g} \]

### Step 2: Calculate the mass of one atom of Nitrogen (Option II)
- The mass of one atom of Nitrogen:
\[ \text{Mass of 1 atom of N} = \frac{14 \text{ g}}{6.022 \times 10^{23}} \approx 2.32 \times 10^{-23} \text{ g} \]

### Step 3: Calculate the mass of \(1 \times 10^{-10}\) moles of Oxygen (Option III)
- The mass of \(1 \times 10^{-10}\) moles of Oxygen:
\[ \text{Mass of } 1 \times 10^{-10} \text{ moles of O} = 1 \times 10^{-10} \text{ moles} \times 16 \text{ g/mol} = 16 \times 10^{-10} \text{ g} = 1.6 \times 10^{-9} \text{ g} \]

### Step 4: Calculate the mass of \(1 \times 10^{-10}\) moles of Copper (Option IV)
- The mass of \(1 \times 10^{-10}\) moles of Copper:
\[ \text{Mass of } 1 \times 10^{-10} \text{ moles of Cu} = 1 \times 10^{-10} \text{ moles} \times 63 \text{ g/mol} = 63 \times 10^{-10} \text{ g} = 6.3 \times 10^{-9} \text{ g} \]

### Summary of Masses:
- Option I (Oxygen atom): \(2.66 \times 10^{-23} \text{ g}\)
- Option II (Nitrogen atom): \(2.32 \times 10^{-23} \text{ g}\)
- Option III (Oxygen, \(1 \times 10^{-10}\) moles): \(1.6 \times 10^{-9} \text{ g}\)
- Option IV (Copper, \(1 \times 10^{-10}\) moles): \(6.3 \times 10^{-9} \text{ g}\)

### Step 5: Arrange in Increasing Order
Now we can arrange these values in increasing order:
1. Option II: \(2.32 \times 10^{-23} \text{ g}\) (Nitrogen)
2. Option I: \(2.66 \times 10^{-23} \text{ g}\) (Oxygen)
3. Option III: \(1.6 \times 10^{-9} \text{ g}\) (Oxygen, \(1 \times 10^{-10}\) moles)
4. Option IV: \(6.3 \times 10^{-9} \text{ g}\) (Copper, \(1 \times 10^{-10}\) moles)

### Final Order:
The final order of increasing mass is:
**II < I < III < IV**