Question

when hydrogen atom jumps from the n=4 state to the n=2 state, a photon is emitted. Calculate \(\Delta') E for the transition. can someone show me the solution for this?

Answer 1

First off, hydrogen atoms have s-orbitals and one lone electron. This makes it a quite a bit easier, when talking quantum states.

Now you're talking about a drop of two states, unfortunately the states you are talking in are not as simple as you might think, look:
http://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Hydrogen_Density_Plots.png/1126px-Hydrogen_Density_Plots.png

This can be described by a set of 4 numbers, called the quantum state:
\[\large( n , \ell , m_\ell , m_s)\]

As anybody who has dabbled in quantum physics can tell you though: the more you know about the position, the less you can tell about it's properties -- the more you know about the properties, the less you know about the position.

Thankfully here, you can drop the properties and all the complexities from the problem itself because the quantum system you have here is very simple. Phew!

So...

\[Energy \approx \large -13.6eV(\frac{1}{n_f^2}-\frac{1}{n_i^2})=-13.6eV\frac{1}{(4)^2}-\frac{1}{(2)^2}\]
1 eV = 1.6022 × 10^-19 Joules

Can you figure it out from here? Post back if you do I'd like to know if it's the correct answer. :-)

Answer 2

Hmm, I'm trying to see if I have initial and final switched. In any case, here ya go:
http://cas.sdss.org/dr6/en/proj/advanced/spectraltypes/energylevels.asp

Answer 3

wait...dont you multiply by -2.18 x10^-18?

Answer 4

-2.18 x10\(^{-18}\) = -13.6 eV *\(\huge\frac{1.6022 \cdot10^{-19} J}{1 eV}\)

Answer 5

Units cancel out ya know :-P

Answer 6

You're left with an answer in Joules.

Answer 7

but i came up with -5.45 x 10^-19 j using -2.18 x 10^-18

Answer 8

Well conversion factor rather, but whatever

Answer 9

Check you parenthesis if you're using a calculator, TI-84's for example don't handle well with arithmetic and scientific notation. The -2.18 number is validated by the equation show just above. I had to type it in myself when I was like, "what the heck is that number?!"

Answer 10

-5.45 x 10\(^{-19}\) J doesn't sound right at all... Not sure where that number came from

Answer 11

What that your final answer? o_O

Answer 12

let me post my solution..wait a minute..

Answer 13

oh lol i see...i forgot to square *facepalm*

Answer 14

i'll try re-solving

Answer 15

A release of about 4 x 10\(^{-19}\) Joules is what I get, can you confirm?

Answer 16

yup that's what i get too

Answer 17

so that's \(\Delta\) E?

Answer 18

That's the change in energy yes, make sure you not it's energy being released by the system (the atom) out into the environment (via a photon)

Answer 19

make sure you note* sry been a long day