# The lifetime of the excited states of a hydrogen atom?

#### sumit_1

How can we differentiate among the lifetimes of the excited states of the hydrogen atom? The states are:
2p, 2s, 3s, 3p

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#### DrClaude

Mentor
What do you mean by "differentiate"?

#### sumit_1

I mean which state out of the given has the highest lifetime and how?

#### mfb

Mentor
You can look them up. You can also calculate them with some knowledge of quantum mechanics and a few integrals. The more precise you want it the more work is necessary.
For rough estimates it is sufficient to find the possible (“allowed”) decay modes.

Is this a homework question?

#### sumit_1

You can look them up. You can also calculate them with some knowledge of quantum mechanics and a few integrals. The more precise you want it the more work is necessary.
For rough estimates it is sufficient to find the possible (“allowed”) decay modes.

Is this a homework question?
Yes, it is a homework question. But how can I do the rough estimates on the basis of decay modes?

#### mfb

Mentor
I moved the thread to our homework section.

Which decay modes are allowed for these states?

#### sumit_1

I moved the thread to our homework section.

Which decay modes are allowed for these states?
I think, it should be gamma decay since in every transition, it will emit a photon.

#### mfb

Mentor
It is only called gamma for nuclear transitions. Photon emission, sure, but what are the possible final states in each case?

#### sumit_1

It is only called gamma for nuclear transitions. Photon emission, sure, but what are the possible final states in each case?
The final state in each case should be 1s.

#### sumit_1

Is the discussion over?

#### DrClaude

Mentor
Is the discussion over?
That's a premature bump. People come and go on PhysicsForums, as many are quite busy in real life.

The final state in each case should be 1s.
Ultimately, yes. But I would imagine that the context is that of electric dipole transitions. What are the selection rules? Also, even if the there is a single final state, can't intermediate processes be observed?

#### sumit_1

That's a premature bump. People come and go on PhysicsForums, as many are quite busy in real life.
That's fine.

Ultimately, yes. But I would imagine that the context is that of electric dipole transitions. What are the selection rules? Also, even if the there is a single final state, can't intermediate processes be observed?
Yes, there can be.

#### mfb

Mentor
So what are these intermediate processes?

Can 2p directly go to 1s? Can 2s? 3s? 3p?
Which intermediate states can be reached in between?

We won't finish your homework for you here, you can only get hints.

#### sumit_1

So what are these intermediate processes?

Can 2p directly go to 1s? Can 2s? 3s? 3p?
Which intermediate states can be reached in between?

We won't finish your homework for you here, you can only get hints.
Yes, I know, I need only hints.
2s can go directly to 1s , but 2p will go to 2s first and then to 1s.
similarly 3s first will come to 2p then it will come to 2s and then 1s.
3p will come to 3s first and then it will follow as described above.
This is just what I am thinking. I don't have any text from which I can read properly.

#### DrClaude

Mentor
2s can go directly to 1s , but 2p will go to 2s first and then to 1s.
similarly 3s first will come to 2p then it will come to 2s and then 1s.
3p will come to 3s first and then it will follow as described above.
That's not correct. What are the dipole selection rules for transitions in the hydrogen atom? (Any decent textbook discussing those transitions will mention the selection rules.)

#### sumit_1

That's not correct. What are the dipole selection rules for transitions in the hydrogen atom? (Any decent textbook discussing those transitions will mention the selection rules.)

"The lifetime of the excited states of a hydrogen atom?"

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