I have a homework for the school to do and it says: Why is the energy of the electron in the atom of hydrogen negative?
Any help plz?

5 COMMENTS

The energy is not negative, the charge is. The signs of charges were labeled by Benjamin Franklin, and were arbitrary. There is nothing mathematically “negative” about electrons, or “positive” about protons; they just have equal and opposite charges.

the author said:
The names positive and negative were coined by Benjamin Franklin. Franklin found that charge behaves like positive and negative numbers.
So what is positive and what is negative? It’s entirely up to us! Franklin established the convention that a glass rod that has been rubbed with silk is positively charged; and a plastic rod rubbed with wool is negative.
So it’s only by convention electrons have a negative charge and protons a positive charge.

The other answers seem to be confusing charge with energy.
The answer is: Because it’s in a bound state, and all bound states have negative energy relative to the unbound reference state.
Two objects are usually defined to have zero potential energy relative to each other when they’re so far apart that their interactions are negligible–strictly speaking, they’re taken to be infinitely far apart. This is the unbound reference state, the state that’s usually defined to have zero energy. If they repel each other, as you move them closer together it takes work to do this, and the potential energy is positive. But if they attract each other, as they move closer together the potential energy goes lower and lower. And since it started at zero, the potential energy is negative.
The electron also has kinetic energy, but it’s smaller in magnitude than the potential energy (by a factor of 2 for a hydrogen atom; it comes from the inverse-square law). So the total energy (kinetic + potential) is negative.
All it’s saying is that you’d have to add energy to it to bring it to the reference state, in other words, to remove the electron from the atom.

Like any potential energy, the electron’s energy is RELATIVE to some arbitrary reference point. Consider gravitational potential energy. if you measure it from the ground, it’s positive above ground. But if you measure it from infinity, it’s negative as you get closer.
The coulomb potential between opposite attracting charges is just like the gravitational potential–if you set it to zero at infinity, it is negative inside.
Now the electron has kinetic energy as well. If that kinetic energy is greater in magnitude than the negative potential, then the total energy is positive and the electron is not bound–like a particle in a gravitational field that has more than escape velocity. But if the electron is bound to an atom, the total energy must be negative.
So the short answer is–the electron’s energy is negative because it is bound to the atom.

The energy is not negative, the charge is. The signs of charges were labeled by Benjamin Franklin, and were arbitrary. There is nothing mathematically “negative” about electrons, or “positive” about protons; they just have equal and opposite charges.

the author said:

The names positive and negative were coined by Benjamin Franklin. Franklin found that charge behaves like positive and negative numbers.

So what is positive and what is negative? It’s entirely up to us! Franklin established the convention that a glass rod that has been rubbed with silk is positively charged; and a plastic rod rubbed with wool is negative.

So it’s only by convention electrons have a negative charge and protons a positive charge.

Not all exactly. Some electrons are positive =these type of electrons are called positrons.

So electrons live in the world of positives and negatives.

The other answers seem to be confusing charge with energy.

The answer is: Because it’s in a bound state, and all bound states have negative energy relative to the unbound reference state.

Two objects are usually defined to have zero potential energy relative to each other when they’re so far apart that their interactions are negligible–strictly speaking, they’re taken to be infinitely far apart. This is the unbound reference state, the state that’s usually defined to have zero energy. If they repel each other, as you move them closer together it takes work to do this, and the potential energy is positive. But if they attract each other, as they move closer together the potential energy goes lower and lower. And since it started at zero, the potential energy is negative.

The electron also has kinetic energy, but it’s smaller in magnitude than the potential energy (by a factor of 2 for a hydrogen atom; it comes from the inverse-square law). So the total energy (kinetic + potential) is negative.

All it’s saying is that you’d have to add energy to it to bring it to the reference state, in other words, to remove the electron from the atom.

Like any potential energy, the electron’s energy is RELATIVE to some arbitrary reference point. Consider gravitational potential energy. if you measure it from the ground, it’s positive above ground. But if you measure it from infinity, it’s negative as you get closer.

The coulomb potential between opposite attracting charges is just like the gravitational potential–if you set it to zero at infinity, it is negative inside.

Now the electron has kinetic energy as well. If that kinetic energy is greater in magnitude than the negative potential, then the total energy is positive and the electron is not bound–like a particle in a gravitational field that has more than escape velocity. But if the electron is bound to an atom, the total energy must be negative.

So the short answer is–the electron’s energy is negative because it is bound to the atom.