Atom's mass -- does it change with energy levels?

• B
• jeremyfiennes
In summary: There is no frame in which photon is at rest, so @jeremyfiennes you can't use this equation to describe a photon.In summary, an atom in an excited state has a higher mass than when in its ground state.
jeremyfiennes
TL;DR Summary
Does an atom in an excited state have a higher mass than when in its ground state?
Summary: Does an atom in an excited state have a higher mass than when in its ground state?

Summary: Does an atom in an excited state have a higher mass than when in its ground state?

Does an atom in an excited state have a higher mass than when in its ground state?

Yes. m = E/c2

So the photon which was absorbed and provided the additional excited state mass, also has mass.

jeremyfiennes said:
So the photon which was absorbed and provided the additional excited state mass, also has mass.

No, the energy from the photon has been converted into mass.

DaveE said:
Yes. m = E/c2

Assuming that we are working in a reference frame in which atom is at rest. There is no frame in which photon is at rest, so @jeremyfiennes you can't use this equation to describe a photon. General formula looks like this: ##m=\frac{1}{c^2}\sqrt{E^2-c^2\vec{p}^2}##. For a single photon ##E=c|\vec{p}|##, so ##m=0##.

DaveE
So E=mc^2 doesn't apply to photons, which have energy but no mass?

##mc^2## is called rest energy and should be written as ##E_0## with a subscript. And only in a frame in which object is at rest we have ##E=E_0##. Photons are never at rest so we can't talk about their rest energy. General formula involves momentum, as I stated in my last post.

Electrons orbiting at 99.9% of the speed of light have energy and corresponding E=mc^2 mass. So why don't photons traveling at 100% of the speed of light. I don't get the distinction.

jeremyfiennes said:
Electrons orbiting at 99.9% of the speed of light have energy and corresponding E=mc^2 mass.

No. Putting aside the fact, that in QM you can't talk about the speed of electron orbiting a nucleus, in a reference frame in which electron has speed ##0.999c## you can't use ##E=mc^2##. You have to use general formula ##m=\frac{1}{c^2}\sqrt{E^2-c^2\vec{p}^2}##, because in this reference frame momentum ##\vec{p}## is non-zero. Read carefully what I wrote:

weirdoguy said:
And only in a frame in which object is at rest we have ##E=E_0##.

Thanks. I will have to think. In the meantime: why can't one talk of the speed of an electron?

jeremyfiennes said:
Thanks. I will have to think. In the meantime: why can't one talk of the speed of an electron?
You can, and I’m not seeing where anyone said you can’t.

What you cannot do is use the classical formulas ##p=mv## (momentum) and ##E=mv^2/2## (kinetic energy) when ##v## is not small compared with ##c##, nor the relativistic ##E=mc^2## when ##v## is non-zero.

jeremyfiennes said:
Thanks. I will have to think. In the meantime: why can't one talk of the speed of an electron?

You can talk about the speed of an electron. You can't talk about the speed of an electron orbiting a nucleus, because the electron isn't orbiting the nucleus like a little planet. That's the Bohr model of the atom and it is known not to be a valid description.

jeremyfiennes said:
Electrons orbiting at 99.9% of the speed of light have energy and corresponding E=mc^2 mass.
In the expression ##mc^2##, ##m## for most physicists these days is what used to be called the "rest mass". So the expression ##E = mc^2## is the amount of energy the electron has when it is at rest.

When it's moving, it has kinetic energy in addition to the rest energy.

But that energy is bound up in a sense in the form of the mass. If the electron meets a positron, both particles will annihilate and then you'll have the energy available. But the mass will be gone.

jeremyfiennes said:
So why don't photons traveling at 100% of the speed of light. I don't get the distinction.

Photons are missing the "rest energy" because photons are never at rest.

weirdoguy
jeremyfiennes said:
So the photon which was absorbed and provided the additional excited state mass, also has mass.
No, mass isn’t additive. The mass of a combined object is equal or greater than the masses of its constituents.

jeremyfiennes said:
why can't one talk of the speed of an electron?

You really should pay attention to every word in a sentence... In the beggining I was talking about electron in a quantum mechanical atom, not free electron. In an atom things are not that easy.

Last edited:

1. What is the relationship between an atom's mass and its energy levels?

An atom's mass does not change with its energy levels. The mass of an atom is determined by the total number of protons and neutrons in its nucleus, which remains constant regardless of the energy level of the electrons orbiting the nucleus.

2. Can an atom's mass change when it gains or loses energy?

No, an atom's mass does not change when it gains or loses energy. The mass of an atom is a fundamental property and is not affected by changes in energy levels.

3. How does Einstein's famous equation, E=mc², relate to an atom's mass and energy?

Einstein's equation, E=mc², explains the relationship between an object's mass and its energy. It states that mass and energy are equivalent and can be converted into one another. However, this does not mean that an atom's mass changes with energy levels.

4. Can an atom's mass change during a chemical reaction or nuclear reaction?

During a chemical reaction, the atoms involved may rearrange their electrons, but the total number of protons and neutrons remains the same. Therefore, the mass of the atoms does not change. In a nuclear reaction, however, the number of protons and neutrons in the nucleus may change, resulting in a change in the atom's mass.

5. How do scientists measure the mass of an atom?

Scientists use a unit called the atomic mass unit (amu) to measure the mass of an atom. This unit is defined as 1/12th the mass of a carbon-12 atom, which has 6 protons and 6 neutrons in its nucleus. The mass of an atom is determined by comparing it to the mass of a carbon-12 atom using a mass spectrometer.

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