The energy necessary to remove the electron from `n=10` state hydrogen atom will be

Options

A. 1.36 e V
B. 0.0135 e V
C. 13.6 e V
D. 0.136 e V

Explanation

To find the energy necessary to remove the electron from the \( n = 10 \) state of a hydrogen atom, we can follow these steps:

### Step 1: Understand the Energy Levels of Hydrogen
The energy of an electron in a hydrogen atom at a principal quantum number \( n \) is given by the formula:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
where \( E_n \) is the energy at level \( n \) and \( Z \) (the atomic number for hydrogen) is 1.

### Step 2: Calculate the Energy at \( n = 10 \)
Substituting \( n = 10 \) into the formula:
\[ E_{10} = -\frac{13.6 \, \text{eV}}{10^2} = -\frac{13.6 \, \text{eV}}{100} = -0.136 \, \text{eV} \]

### Step 3: Determine the Energy Required to Remove the Electron
To remove the electron from the \( n = 10 \) state, we need to bring it to the point where the energy is zero (which is the energy at infinity, \( E_{\infty} = 0 \)):
\[ \text{Energy required} = E_{\infty} - E_{10} \]
Substituting the values:
\[ \text{Energy required} = 0 - (-0.136 \, \text{eV}) = 0.136 \, \text{eV} \]

### Conclusion
The energy necessary to remove the electron from the \( n = 10 \) state of a hydrogen atom is \( 0.136 \, \text{eV} \).

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