In the nth orbit, the energy of an electron `E_(n)= -( 13.6)/(n^(2)) eV` for hydrogen atom. The energy required to take the electron from first orbit to second orbit will be

Options

A. `10. 2 eV`
B. `12.1 eV`
C. `13.6 eV`
D. `3.4 eV`

Explanation

To find the energy required to take the electron from the first orbit to the second orbit in a hydrogen atom, we can follow these steps:

### Step 1: Write down the formula for energy in the nth orbit
The energy of an electron in the nth orbit of a hydrogen atom is given by the formula:
\[ E_n = -\frac{13.6}{n^2} \text{ eV} \]

### Step 2: Calculate the initial energy (E1) in the first orbit
For the first orbit (n = 1):
\[ E_1 = -\frac{13.6}{1^2} = -13.6 \text{ eV} \]

### Step 3: Calculate the final energy (E2) in the second orbit
For the second orbit (n = 2):
\[ E_2 = -\frac{13.6}{2^2} = -\frac{13.6}{4} = -3.4 \text{ eV} \]

### Step 4: Calculate the energy required to move from the first orbit to the second orbit
The energy required (ΔE) to move the electron from the first orbit to the second orbit is given by:
\[ \Delta E = E_f - E_i = E_2 - E_1 \]
Substituting the values we calculated:
\[ \Delta E = -3.4 \text{ eV} - (-13.6 \text{ eV}) = -3.4 + 13.6 = 10.2 \text{ eV} \]

### Final Answer
The energy required to take the electron from the first orbit to the second orbit is:
\[ \Delta E = 10.2 \text{ eV} \]

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