In hydrogen atom, energy of first excited state is `- 3.4 eV`. Then, `KE` of the same orbit of hydrogen atom is.

Options

A. `+ 3.4 eV`
B. `+6.8 eV`
C. `-13.6 eV`
D. `+13.6 eV`

Explanation

To find the kinetic energy (KE) of the hydrogen atom in the first excited state, we can follow these steps:

### Step 1: Identify the quantum number for the first excited state
The first excited state of a hydrogen atom corresponds to the quantum number \( n = 2 \). The ground state corresponds to \( n = 1 \), and the first excited state is the next level up.

**Hint:** Remember that the ground state is always \( n = 1 \), and the first excited state is \( n = 2 \).

### Step 2: Use the formula for total energy in a hydrogen atom
The total energy \( E \) of an electron in a hydrogen atom is given by the formula:
\[ E = -\frac{13.6 \, \text{eV} \cdot Z^2}{n^2} \]
For hydrogen, \( Z = 1 \). Therefore, the formula simplifies to:
\[ E = -\frac{13.6 \, \text{eV}}{n^2} \]

**Hint:** The formula for total energy is derived from the Bohr model of the hydrogen atom.

### Step 3: Calculate the total energy for \( n = 2 \)
Substituting \( n = 2 \) into the formula:
\[ E = -\frac{13.6 \, \text{eV}}{2^2} = -\frac{13.6 \, \text{eV}}{4} = -3.4 \, \text{eV} \]
This confirms that the total energy at the first excited state is indeed \( -3.4 \, \text{eV} \).

**Hint:** Make sure to square the value of \( n \) when substituting into the formula.

### Step 4: Relate total energy to kinetic energy
In the hydrogen atom, the kinetic energy (KE) is related to the total energy (E) by the equation:
\[ KE = -\frac{E}{2} \]
This means that the kinetic energy is half the magnitude of the total energy (but positive).

**Hint:** Remember that kinetic energy is always a positive quantity.

### Step 5: Calculate the kinetic energy
Using the total energy we found:
\[ KE = -\frac{-3.4 \, \text{eV}}{2} = \frac{3.4 \, \text{eV}}{2} = 1.7 \, \text{eV} \]

**Hint:** When calculating kinetic energy, ensure you take the absolute value of the total energy.

### Final Answer
The kinetic energy of the hydrogen atom in the first excited state is \( 1.7 \, \text{eV} \).