Question

If energy of an electron in the first orbit is -13.6 eV, then predict the amount of energy required to transfer it to the fourth orbit.

• A. 2.55 eV
• B. 12.75 eV
• C. 12.75 eV
• D. 2.55 eV

Hint:

To find the energy required to move an electron between orbits, use the formula \( E_n = - \frac{13.6}{n^2} \).

Answer 1

The Correct Option is B

The energy of an electron in the nth orbit is given by: 
\[ E_n = - \frac{13.6}{n^2} \, \text{eV}. \] The energy in the first orbit (\(n = 1\)) is: \[ E_1 = - \frac{13.6}{1^2} = -13.6 \, \text{eV}. \] The energy in the fourth orbit (\(n = 4\)) is: \[ E_4 = - \frac{13.6}{4^2} = - \frac{13.6}{16} = -0.85 \, \text{eV}. \] The energy required to transfer the electron from the first orbit to the fourth orbit is: \[ \Delta E = E_4 - E_1 = -0.85 - (-13.6) = 12.75 \, \text{eV}. \]