Question

The energy of the nth orbit of the hydrogen atom is given by: \[ E_n = - \frac{13.6}{n^2} \, \text{eV} \] What is the energy of the second orbit (n = 2) of the hydrogen atom?

• A. \( - 3.4 \, \text{eV} \)
• B. \( - 13.6 \, \text{eV} \)
• C. \( - 6.8 \, \text{eV} \)
• D. \( - 1.36 \, \text{eV} \)

Hint:

The energy of an electron in the hydrogen atom depends on the square of the principal quantum number \( n \). The energy becomes less negative (closer to zero) as \( n \) increases.

Answer 1

The Correct Option is A

We are given the energy of the nth orbit of the hydrogen atom by the equation: \[ E_n = - \frac{13.6}{n^2} \, \text{eV} \] For the second orbit (\( n = 2 \)): \[ E_2 = - \frac{13.6}{2^2} = - \frac{13.6}{4} = - 3.4 \, \text{eV} \] Thus, the energy of the second orbit is \( - 3.4 \, \text{eV} \).