1. Total energy = Kinetic + Potential
QUESTION:
For Bohr’s model, the energy of an electron in any of the orbits is a negative value. This means that… A. the electron is moving in a clockwise direction B. the electron is moving counterclockwise C. the electron has imaginary speed D. none of these
Total energy = Kinetic + Potential
Kinetic energy = ½ (mass) (speed)2, can’t be negative
Potential energy depends on location and is arbitrarily defined. When dealing with atoms, it is customary to define PE=0 when electron is at infinite distance from the nucleus.
If: KE + PE < 0, then PE < 0,
Electron converts KE to PE to move from location with lower PE to one with higher PE. If not enough KE,
external energy source (light) is needed.
SCRIPT
For Bohr’s model, the energy of an electron in any of the orbits is a negative value. This means that… A. the electron is moving in a clockwise direction B. the electron is moving counterclockwise C. the electron has imaginary speed D. none of these
PAUSE
Energy has nothing to do with the direction of motion. SO we can immediately rule out choices A and B .
Speed is a real number. In fact, it can only be positive or negative. SO we can also rule out C.
The correct answer is D.
SO what does a negative energy actually mean?
First of all when we talk about the energy of an electron, we’re talking about the total energy, which is the sum of kinetic and potential energy.
Kinetic energy is defined as the energy due to motion and by the formula one half times mass times the square of the speed.
Since mass is always positive,…
and speed is zero or positive…
Kinetic energy cannot be a negative number.
On the other hand, potential energy depends on location and is arbitrarily defined. It can be positive or negative.
CALLOUT (Positive or zero) pointing to “KE” in “KE + PE < 0”
In the case of atoms, it is customary to define the potential energy of an electron to be zero when it is at infinite distance from the nucleus.
This means that the potential energy of the electron must be negative, if the total energy is negative.
HIGHLIGHT “PE < 0”
CALLOUT “Negative” pointing to PE in “KE+PE < 0”
You need to add a negative number to a positive number to get a negative sum.
But what does a negative potential energy mean? Simply… any object must convert kinetic energy to potential energy
In order to increase its potential energy. If there isn’t enough kinetic energy, then energy from an external source,
Such as light, is needed.
CLICK Here’s a diagram that shows the energies of the electron in the first four orbits.
CALLOUT (n=3 an n=4) pointing to third and fourth level.
According to Bohr’s model, the energy of the electron in the nth orbit is given by
E equals –13.6 electron volts, divided by n squared.
So when n equals 1, the energy is –13.6 electron volts.
When n equals 2, the energy is –13.6 electron volts, divided by 2 squared,…
Or –13.6 electron volts, divided by 4.
CLICK Bohr defined zero energy as the potential energy of the electron when it is at infinite distance away from the nucleus.
Therefore, if we were to provide an extra 13.6 eV of energy to an electron in the first orbit…
CLICK
The electron will gain enough energy to be free itself from the nucleus,…. That is…to move an infinite distance away from the nucleus.
This would be the minimum energy needed to remove the electron from the atom, and is known as the ionization energy. If you provided more energy than this,
the extra energy will just add to the kinetic energy of the free electron.
CLICK If an electron happens to be in the second orbit, then you won’t need as much energy to remove it from the atom.
You will only need ¼ ot 13.6 electron volts.
CLICK PAUSE
END RECORDING

2. -13.6 eV
E = n2

3. Video ID: © 2008, Project VALUE (Video Assessment Library for Undergraduate Education), Department of Physical Sciences Nicholls State University Author: Glenn V. Lo Funded by Louisiana Board of Regents Contract No. LA-DL-SELECT-13-07/08