# Negative M.E.

1. Jun 13, 2008

### ritwik06

What is the significance of negative mechanical eneregy of a body?
Eg. electron in 1st orbit of H atom

2. Jun 13, 2008

### Mapes

It just means that the reference energy level (the "zero") is taken at a higher level. In this case, the reference is conventionally taken to be an electron at an infinite distance from the nucleus.

3. Jun 14, 2008

### dynamicsolo

In describing the total mechanical energy of a system, a negative value is interpreted as meaning that the system is bound; that is to say, the total kinetic energy of all the particles (which is non-negative) has a smaller magnitude than the total potential energy of the fields between them. So there is not enough kinetic energy for members of the system to separate to limitless distances.

An example is the total mechanical energy for a satellite in, say, a circular orbit around a planet. If the masses of satellite and planet are m and M>>m, respectively, and the radius of the orbit is R, then the kinetic energy of the satellite is

(1/2)·m·(v^2) = GmM/2R ,

while the gravitational potential energy of the field is

-GmM/R .

Thus, the total mechanical energy for the system is

-GmM/2R .

(We are treating the mass of the planet as effectively infinite here for simplicity. We really should use "reduced mass" for the system.)

A similar result is found for other sorts of systems bound by forces which can be described by potential functions.

4. Jun 15, 2008

### ritwik06

Thanks a lot. I have understood it quite right. thanks for the help once agin.