If the value of `E=-78.4 "kcal//mol"`, the order of the orbit in hydrogen atom is-

Options

A. `4`
B. `3`
C. `2`
D. `1`

Explanation

To find the order of the orbit (n) in a hydrogen atom given the energy value \( E = -78.4 \, \text{kcal/mol} \), we can follow these steps:

### Step 1: Understand the energy formula
The energy of an electron in a hydrogen atom is given by the formula:
\[ E = -\frac{13.6 \, Z^2}{n^2} \, \text{eV} \]
where \( Z \) is the atomic number (for hydrogen, \( Z = 1 \)) and \( n \) is the principal quantum number (the order of the orbit).

### Step 2: Convert the energy from kcal/mol to eV
First, we need to convert the energy from kilocalories per mole to electron volts (eV). The conversion factor is:
\[ 1 \, \text{kcal/mol} \approx 0.0434 \, \text{eV} \]
Thus, we convert \( -78.4 \, \text{kcal/mol} \):
\[ E = -78.4 \, \text{kcal/mol} \times 0.0434 \, \text{eV/kcal/mol} \approx -3.404 \, \text{eV} \]

### Step 3: Set up the equation with the known values
Now we can substitute \( E \) and \( Z \) into the energy formula:
\[ -3.404 = -\frac{13.6 \times 1^2}{n^2} \]
This simplifies to:
\[ 3.404 = \frac{13.6}{n^2} \]

### Step 4: Rearrange to solve for \( n^2 \)
Rearranging the equation gives:
\[ n^2 = \frac{13.6}{3.404} \]

### Step 5: Calculate \( n^2 \)
Calculating the right side:
\[ n^2 \approx \frac{13.6}{3.404} \approx 4 \]

### Step 6: Take the square root to find \( n \)
Taking the square root of both sides:
\[ n \approx 2 \]

### Conclusion
The order of the orbit in the hydrogen atom is \( n = 2 \).

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