Energy Levels in the Hydrogen Atom

The energy levels in the hydrogen atom are described by the equation En = 13.6/n^2, where En is the energy of the nth orbit and n is the principal quantum number. This equation, known as the Bohr model, provides a simplified description of the energy levels in the hydrogen atom.

Explanation of the Equation

The equation En = 13.6/n^2 represents the energy of the electron in the nth orbit of a hydrogen atom. The energy is negative, indicating that the electron is bound to the nucleus. The energy levels become closer together as n increases, which means that the energy required to move from one level to another decreases.

Energy Required to Transition between Orbits

To determine the energy required to move from the first orbit (n=1) to the second orbit (n=2), we can subtract the energy of the initial orbit (E1) from the energy of the final orbit (E2).

E2 - E1 = 13.6/n2 - 13.6/n1

For the first orbit, n1 = 1, and for the second orbit, n2 = 2.

E2 - E1 = 13.6/2^2 - 13.6/1^2
= 13.6/4 - 13.6/1
= 3.4 - 13.6
= -10.2 eV

The negative sign indicates that energy is released when the electron transitions from the first to the second orbit. In this case, the energy released is 10.2 electron volts (eV).

Conclusion

The energy required to take an electron from the first orbit to the second orbit in a hydrogen atom is 10.2 eV. This energy can be calculated using the equation En = 13.6/n^2, which describes the energy levels in the hydrogen atom. The negative sign indicates that energy is released during the transition.