Energy of electron in its nth orbit is given by `(E_n=-(13.6)/n^2 xxz)ev` . Consider a hydrogen atom , find the amount of energy needed to transfer electron from 1st orbit to 3rd orbit:

Options

A. 13.6 eV
B. 1.51 eV
C. 3.4 eV
D. 12.09 eV

Answer

To find the amount of energy needed to transfer an electron from the first orbit (n=1) to the third orbit (n=3) in a hydrogen atom, we can use the formula for the energy of an electron in the nth orbit:

\[ E_n = -\frac{13.6}{n^2} \text{ eV} \]

### Step 1: Calculate the energy of the electron in the first orbit (n=1)

Using the formula:

\[ E_1 = -\frac{13.6}{1^2} = -13.6 \text{ eV} \]

### Step 2: Calculate the energy of the electron in the third orbit (n=3)

Using the formula:

\[ E_3 = -\frac{13.6}{3^2} = -\frac{13.6}{9} \text{ eV} \]

Calculating this gives:

\[ E_3 = -1.51 \text{ eV} \quad (\text{approximately}) \]

### Step 3: Calculate the change in energy (ΔE)

The change in energy when moving from the first orbit to the third orbit is given by:

\[ \Delta E = E_3 - E_1 \]

Substituting the values we calculated:

\[ \Delta E = \left(-1.51 \text{ eV}\right) - \left(-13.6 \text{ eV}\right) \]

This simplifies to:

\[ \Delta E = -1.51 + 13.6 = 12.09 \text{ eV} \]

### Conclusion

The amount of energy needed to transfer the electron from the first orbit to the third orbit is approximately **12.09 eV**.

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