`1.8 g` of hydrogen is excite by irradiation. The study of spectra indicated that `27 %` of the atoms are in the first excite state, `15 %` of the aton in the second excited, and the rest in the ground state. The ground stat, ionization energy of hydrogen atom is `21.4 xx 10^(-12)`ergs.
The number of atoms present in the second excited state is

Options

A. `1.61 xx 10^(23)`
B. `0.805 xx 10^(23)`
C. `2.92 xx 10^(23)`
D. `1.46 xx 10^(23)`

Explanation

To solve the problem step by step, we need to follow these calculations:

### Step 1: Calculate the number of moles of hydrogen
The number of moles (n) can be calculated using the formula:
\[ n = \frac{\text{mass}}{\text{molar mass}} \]

Given:
- Mass of hydrogen = 1.8 g
- Molar mass of hydrogen (H₂) = 2 g/mol

So,
\[ n = \frac{1.8 \, \text{g}}{2 \, \text{g/mol}} = 0.9 \, \text{mol} \]

### Step 2: Calculate the total number of hydrogen atoms
Using Avogadro's number (\( N_A = 6.022 \times 10^{23} \, \text{atoms/mol} \)), we can find the total number of atoms:
\[ \text{Total atoms} = n \times N_A \]
\[ \text{Total atoms} = 0.9 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \]
\[ \text{Total atoms} \approx 5.42 \times 10^{23} \, \text{atoms} \]

### Step 3: Calculate the number of atoms in the second excited state
We know that 15% of the total atoms are in the second excited state. Therefore, we can calculate the number of atoms in the second excited state as follows:
\[ \text{Atoms in second excited state} = 0.15 \times \text{Total atoms} \]
\[ \text{Atoms in second excited state} = 0.15 \times 5.42 \times 10^{23} \]
\[ \text{Atoms in second excited state} \approx 8.13 \times 10^{22} \, \text{atoms} \]

### Final Answer
The number of atoms present in the second excited state is approximately \( 8.13 \times 10^{22} \, \text{atoms} \).

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