What is the energy required to remove an electron in a hydron atom from n=10 stat?

Options

A. 13.6eV
B. 1.36eV
C. 0.136eV
D. 0.0136eV

Explanation

To find the energy required to remove an electron from the n=10 state in a hydrogen atom, we can use the formula for the energy of an electron in a hydrogen atom:

### Step-by-Step Solution:

1. **Identify the Formula**:
The energy of an electron in a hydrogen atom in the nth orbit is given by the formula:
\[ E_n = -\frac{13.6 \, \text{eV} \cdot Z^2}{n^2} \]
where \( Z \) is the atomic number (for hydrogen, \( Z = 1 \)) and \( n \) is the principal quantum number (in this case, \( n = 10 \)).

2. **Substitute the Values**:
For hydrogen, substitute \( Z = 1 \) and \( n = 10 \):
\[ E_{10} = -\frac{13.6 \, \text{eV} \cdot 1^2}{10^2} \]

3. **Calculate the Energy**:
\[ E_{10} = -\frac{13.6 \, \text{eV}}{100} = -0.136 \, \text{eV} \]

4. **Interpret the Result**:
The negative sign indicates that the electron is bound to the atom. To remove the electron from this state (to ionize it), we need to provide energy equal to the absolute value of this energy:
\[ \text{Energy required} = 0.136 \, \text{eV} \]

### Final Answer:
The energy required to remove an electron from the n=10 state in a hydrogen atom is **0.136 eV**.