# Bohr Model and Energy

A) From the Bohr model of the Hydrogen atom, calculate the minimum amount of energy (in eV) an electron in the lowest orbital would need to free it from its proton (i.e., to ionize the atom).

B) If you consider the Bohr model of the atom, where the proton and electron act as two bodies of mass, and the electron escapes from the pull of the proton with the energy found in part A, how is this similar to the energy needed for one body of mass, like a planet, to escape the gravitational force of another planet? Explain your answer.

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A) Let us consider a hydrogen atom with a single electron revolving around the nucleus containing a single
proton. The centripetal force required for the circular motion of the electron is provided by the electrostatic
force between the proton and the electron. Hence,

mv2/r = (1/4Πε0)exe/r2 = (1/4Πε0)e2/r2

Or mv2 = (1/4Πε0)e2/r ……..(1)

Or kinetic energy KE = ½ mv2 = (1/8Πε0)e2/r ……….(2)

According to Bohr’s atomic model, the electron can occupy only those orbits in which its angular momentum
is an integral multiple of h/2Π or mvr = nh/2Π

For the first orbit, n = 1. Hence, mvr = h/2Π or v = h/2Πmr

Substituting in (1) …

Solution Summary
The step by step solution explains how to use the Bohr model to calculate the minimum energy to ionize a hydrogen atom.

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