The energy required to dislodge electron from excited isolated H-atom `(IE_(1) = 13.6 eV)` is

Options

A. `= 13.6 eV`
B. `gt 13.6 eV`
C. `lt 13.6` and `gt 3.4 eV`
D. `le 3.4 eV`

Explanation

To solve the problem of determining the energy required to dislodge an electron from an excited isolated hydrogen atom, we can follow these steps:

### Step 1: Understand the Ionization Energy
The ionization energy (IE) for a hydrogen atom in its ground state (n=1) is given as 13.6 eV. This is the energy required to remove the electron from the ground state.

### Step 2: Identify the Excited State
In this problem, we are interested in the excited state of the hydrogen atom. The first excited state corresponds to n=2.

### Step 3: Use the Energy Formula
The energy of an electron in a hydrogen atom at a given energy level (n) can be calculated using the formula:
\[ E_n = -\frac{13.6 \text{ eV}}{n^2} \]

### Step 4: Calculate the Energy for n=2
Substituting n=2 into the formula:
\[ E_2 = -\frac{13.6 \text{ eV}}{2^2} = -\frac{13.6 \text{ eV}}{4} = -3.4 \text{ eV} \]

### Step 5: Determine the Energy Required for Ionization
To remove the electron from the n=2 state, we need to provide enough energy to overcome the negative energy value:
- The energy required to ionize the electron from n=2 to free state (where energy is 0) is:
\[ \text{Energy required} = 0 - (-3.4 \text{ eV}) = 3.4 \text{ eV} \]

### Conclusion
Thus, the energy required to dislodge the electron from the excited isolated hydrogen atom (n=2) is **3.4 eV**.

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