Rearrange the following (I to IV) in the order of increasin masses and choose the correct answer from (A), (B), (C) and (D)
(At. Mass N=14, O=16, Cu=63)
(I) 1 molecule of O
(II) 1 atom of nitrogen
(III) `1xx10^(-10)`g molecular mass of oxygen
(IV) `1xx10^(-7)` atomic mass of copper.

Options

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

Explanation

To solve the problem of rearranging the given options in the order of increasing masses, we need to calculate the mass of each option based on the provided atomic masses and molecular weights. Let's go through each step systematically.

### Step 1: Calculate the mass of 1 molecule of Oxygen (I)
1. **Molecular mass of O2**: Since one molecule of O2 consists of two oxygen atoms, the molecular mass is:
\[ \text{Molecular mass of O2} = 2 \times 16 = 32 \text{ g/mol} \]
2. **Mass of 1 molecule of O2**: To find the mass of one molecule, we divide the molecular mass by Avogadro's number (NA = \(6.022 \times 10^{23}\)):
\[ \text{Mass of 1 molecule of O2} = \frac{32 \text{ g/mol}}{6.022 \times 10^{23}} \approx 5.31 \times 10^{-23} \text{ g} \]

### Step 2: Calculate the mass of 1 atom of Nitrogen (II)
1. **Atomic mass of Nitrogen**: Given as 14 g/mol.
2. **Mass of 1 atom of Nitrogen**: Similar to the previous calculation, we divide the atomic mass by Avogadro's number:
\[ \text{Mass of 1 atom of N} = \frac{14 \text{ g/mol}}{6.022 \times 10^{23}} \approx 2.32 \times 10^{-24} \text{ g} \]

### Step 3: Calculate the mass of \(1 \times 10^{-10}\) g molecular mass of Oxygen (III)
1. **Molecular mass of O2**: As calculated before, the molecular mass is 32 g/mol.
2. **Mass of \(1 \times 10^{-10}\) g molecule of O2**: Since \(1 \times 10^{-10}\) g corresponds to \(1 \times 10^{-10}\) moles of O2, we can calculate:
\[ \text{Mass} = 1 \times 10^{-10} \text{ moles} \times 32 \text{ g/mol} = 3.2 \times 10^{-9} \text{ g} \]

### Step 4: Given mass of \(1 \times 10^{-7}\) atomic mass of Copper (IV)
1. **Mass of Copper**: Given directly as \(1 \times 10^{-7}\) g.

### Step 5: Compare the masses calculated
1. **Masses calculated**:
- (I) \(5.31 \times 10^{-23}\) g (O2 molecule)
- (II) \(2.32 \times 10^{-24}\) g (N atom)
- (III) \(3.2 \times 10^{-9}\) g (O2 molecule with \(1 \times 10^{-10}\) g)
- (IV) \(1 \times 10^{-7}\) g (Cu atom)

### Step 6: Order the masses
Now we can arrange the masses in increasing order:
- (II) \(2.32 \times 10^{-24}\) g (N atom)
- (I) \(5.31 \times 10^{-23}\) g (O2 molecule)
- (IV) \(1 \times 10^{-7}\) g (Cu atom)
- (III) \(3.2 \times 10^{-9}\) g (O2 molecule with \(1 \times 10^{-10}\) g)

### Final Order
Thus, the order of increasing masses is:
**(II) < (I) < (IV) < (III)**

### Answer
The correct answer is **(B)**.