The ionisation potential of hydrogen from ground state to the first excited state is

Options

A. `-13.6 eV`
B. 13.6 eV
C. `-3.4 eV`
D. 3.4 eV

Explanation

To determine the ionization potential of hydrogen from the ground state to the first excited state, we can follow these steps:

### Step 1: Understand the Concept of Ionization Potential
Ionization potential (or ionization energy) is the energy required to remove an electron from an atom or ion. In the case of hydrogen, we are interested in the energy required to move an electron from the ground state (n=1) to the first excited state (n=2).

### Step 2: Use the Formula for Energy Levels in Hydrogen
The energy levels of the hydrogen atom can be calculated using the formula:
\[ E_n = -\frac{13.6 \text{ eV}}{n^2} \]
where \(E_n\) is the energy of the electron at level \(n\).

### Step 3: Calculate the Energy of the Ground State (n=1)
For the ground state (n=1):
\[ E_1 = -\frac{13.6 \text{ eV}}{1^2} = -13.6 \text{ eV} \]

### Step 4: Calculate the Energy of the First Excited State (n=2)
For the first excited state (n=2):
\[ E_2 = -\frac{13.6 \text{ eV}}{2^2} = -\frac{13.6 \text{ eV}}{4} = -3.4 \text{ eV} \]

### Step 5: Calculate the Ionization Potential from Ground State to First Excited State
The ionization potential from the ground state to the first excited state is the energy difference between these two states:
\[ \text{Ionization Potential} = E_2 - E_1 \]
Substituting the values we calculated:
\[ \text{Ionization Potential} = (-3.4 \text{ eV}) - (-13.6 \text{ eV}) = -3.4 \text{ eV} + 13.6 \text{ eV} = 10.2 \text{ eV} \]

### Final Answer
The ionization potential of hydrogen from the ground state to the first excited state is **10.2 eV**.

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