University of Wisconsin Green Bay

According to the Bohr model of the atom, what is the radius of orbit of an electron in the n=4 orbital of hydrogen? What minimum frequency photon is required to remove the electron from the atom?

  • In introduction to quantum mechanics units, you are introduced to a variety of experimental results involving light, atoms, or constituents of atoms. In most cases, when you look at interactions on these tiny scales, you have a foundations of quantum mechanics problem.

    In this case, you are explicitly asked about the Bohr model of the atom. You have equations that give the radius and energy of each orbit in the Bohr atom, and so this is essentially a one-step or definition problem. If you also recognize the energy conservation component of this problem (photon energy is given to the electron) from the beginning, that is good! But don’t worry if you don’t see all parts at the start of the problem—you will be led to conservation of energy as you progress.

  • Atom with orbitals

    As for most definition problems, a picture is not required to organize the information. However, it may help you to picture the energy transfer.

  • radius and energy equations

    Whenever you are asked about the Bohr model of the atom, begin by checking to see if you have a definition equation for the quantity(s) that you want to understand. In this case, both radius and energy for each orbital are given directly through the above equations. If at this stage you also recognize that you will need to know the energy of a photon (E = hf), that is great. If not, you will come to it as you work the problem.

  • The radius of the nth orbital is given directly by this equation. Scroll down to solve for the minimum frequency of the photon.


    Step 2

    In the second question, the electron is freed from the atom due to interaction with the photon. If you did not previously recognize this as an energy problem, at this stage the fact that you know energy levels of the Bohr atom should suggest to you that you can track energy.

  • The first part of this problem is merely a one-step problem describing the Bohr atom.

    For the second question, you need to recognize that energy must be put into the system in order to free the electron. Just as for Conservation of Energy problems involving mechanical energy, it does not matter what is given and what you are asked to find. Always begin the the core physics of the situation.