To which orbit the electron in ground state in the hydrogen atom will jump after absorbing 12.75 eV energy.

Options

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

Answer

To determine the orbit to which the electron in the ground state of a hydrogen atom will jump after absorbing 12.75 eV of energy, we can follow these steps:

### Step 1: Understand the Energy of the Ground State
The energy of an electron in the nth orbit of a hydrogen atom is given by the formula:
\[ E_n = -\frac{13.6 \, \text{eV} \cdot Z^2}{n^2} \]
For hydrogen, \(Z = 1\) and for the ground state, \(n = 1\):
\[ E_1 = -\frac{13.6 \, \text{eV} \cdot 1^2}{1^2} = -13.6 \, \text{eV} \]

### Step 2: Calculate the Energy After Absorption
The electron absorbs 12.75 eV of energy. The new energy of the electron after absorption is:
\[ E_{\text{final}} = E_1 + \text{Energy absorbed} = -13.6 \, \text{eV} + 12.75 \, \text{eV} \]
Calculating this gives:
\[ E_{\text{final}} = -13.6 + 12.75 = -0.85 \, \text{eV} \]

### Step 3: Set Up the Equation for the New Orbit
Now we need to find out which orbit corresponds to this new energy level. We set up the equation:
\[ -\frac{13.6 \, \text{eV}}{n^2} = -0.85 \, \text{eV} \]
Removing the negative signs, we have:
\[ \frac{13.6}{n^2} = 0.85 \]

### Step 4: Solve for \(n^2\)
Rearranging the equation gives:
\[ n^2 = \frac{13.6}{0.85} \]
Calculating the right side:
\[ n^2 = 16 \]

### Step 5: Find the Value of \(n\)
Taking the square root of both sides:
\[ n = 4 \]

### Conclusion
The electron jumps to the 4th orbit after absorbing 12.75 eV of energy.

### Final Answer
The electron in the ground state of the hydrogen atom will jump to the **4th orbit**.

---