According to Bohr's model of the hydrogen atom, the total energy of an electron in the fir… — JAMB UTME

According to Bohr's model of the hydrogen atom, the total energy of an electron in the first excited state ( $n = 2$ ) is $-3.40\text{ eV}$ . Calculate the electric potential energy of the electron in this state, in electron-volts ( $\text{eV}$ ).

Answer: -6.8 eV

Answer

The electric potential energy of the electron in the first excited state is

-6.80\text{ eV}

In Bohr's model of the hydrogen atom, an electron held in a circular orbit by electrostatic attraction has a kinetic energy

K = -E

and an electric potential energy

U = 2E

. Given a total energy

E = -3.40\text{ eV}

, multiplying by 2 yields

U = -6.80\text{ eV}

Step-by-Step Solution

Identify the relationship between total energy and electric potential energy in the Bohr atomic model.

U = 2E

, where

U

is potential energy and

E

is total energy.

For an inverse-square electrostatic force binding an electron in a circular orbit, the virial theorem dictates that kinetic energy

K = -E

and potential energy

U = 2E

Substitute the given value of total energy

E = -3.40\text{ eV}

to solve for

U

U = 2 \times (-3.40\text{ eV}) = -6.80\text{ eV}

Direct multiplication yields the exact electric potential energy of the bound electron.

Key Concept

Energy components (kinetic, potential, and total energy) of an electron in Bohr's atomic model

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