maths/astronomy question

[reds4ever]

i need a hand (ie. the answer, with workings) with this question.


The energies (En) of the energy levels of the hydrogen atom are approximated by the formula

(En/eV) = - (13.6/n^2)

Where eV is electron volts and n is the energy subscript.

I need to show that radiation that has a wavelenght of 656nm (H alpha) is absorbed when hydrogen atoms make the transition from n=2 to n=3.

I've got as far as E2= -3.4eV and E3=-1.51eV and presumably I need to run the above equation for both energy levels and come up with a difference of 656nm (H alpha)

it's the first set of brackets I don't understand, one (En) is a value and the other (eV) is a unit? How do I arrive at a sensible answer?

I'm 36 and signed on a for an Astronomy course, not this!

[Ramo]

eV is a unit of energy ("electron-volt"). It's the energy an electron gains after being accelerated through a 1 V potential. The formula just means that E_n is -13.6/n² eV.

[Ramo]

In this problem, the idea is if an electron loses energy by switching "orbits," it emits a photon which has an energy of h(nu) (Planck's constant multiplied by the frequency), which is hc/lambda (since the wave length times the frequency of light is the speed of light).

[reds4ever]

Originally posted by Ramo
In this problem, the idea is if an electron loses energy by switching "orbits," it emits a photon which has an energy of h(nu) (Planck's constant multiplied by the frequency), which is hc/lambda (since the wave length times the frequency of light is the speed of light).

Ramo, I know i need Plancks constant, and I understand the emitted energy is at 656 nM and so blocking H alpha, I just don't know where to plug the numbers in.

Whats the deal with eV? Does (En/eV) mean En expressed as electron volts? And n^2 is that 2 and 3 or the values of E2 and E3?

[reds4ever]

Originally posted by Ramo
eV is a unit of energy ("electron-volt"). It's the energy an electron gains after being accelerated through a 1 V potential. The formula just means that E_n is -13.6/n² eV.

Ah, sorry i didn't read the above properly (playing RTW and ALT tabbing), thanks a lot.

The n^2 is 2 or 3 in this case, right?

[Japher]

eV is the energy expressed in electron volts

n is the energy level

calculate the energy values at each level (each n) E=13.6/n^2

take the difference to give you the energy emitted

then plug it into E=hv, and solve for v (the wavelenght)

or something

[Japher]

v= whatever Ramo said

isn't that what Einstein got his nobel prize for?

[reds4ever]

Originally posted by Japher
eV is the energy expressed in electron volts

n is the energy level

calculate the energy values at each level (each n) E=13.6/n^2

take the difference to give you the energy emitted

then plug it into E=hv, and solve for v (the wavelenght)

or something

Cheers Japher

it's more the notation i'mtrying to understand, I know whats happening and what i need to prove, but......

[Japher]

am I wrong? I have no idea.

[reds4ever]

Originally posted by Japher
am I wrong? I have no idea.

Neither have I, thats my problem

[Japher]

What? I understand the equations, what don't you understand?

[Japher]

the problem I think you are seeing is that the value n has no units. Thus, by them putting that eV there it supplies the units. What they should of said is

E sub n = (1/n2^2)-(1/n1^2)... with the resulting value having the units eV

[reds4ever]

Originally posted by Japher
the problem I think you are seeing is that the value n has no units. Thus, by them putting that eV there it supplies the units. What they should of said is

E sub n = (1/n2^2)-(1/n1^2)... with the resulting value having the units eV

Thats it! n = -3.4 or whatever.

The way you put it is much clearer,

Cheers, stick around I've got 9 more months of this

[reds4ever]

Does then the Expression (En/eV) literally mean En expressed as eV? I've never come across that before.

i was looking at dividing En (a value) by eV (a unit)

[Japher]

Thats it! n = -3.4 or whatever.

The way you put it is much clearer,

Cheers, stick around I've got 9 more months of this

No! It's not

(E sub n) is a value, the sub n indicates that it is E (energy) at a certain level (n)... At level 1 it is Esub1 at level 2 it is Esub2.... the sub part is only an indicator to denote that it E being "represented" at that state.

Thus, at n=2 you have Esub2 at n=3 you have Esub3

the equation says that Esub2=-13.6/(2*2) and it has the units of eV

Esub3 = -13.6/(3*3) and has the units eV

rarely would you see a n=2.3, or whatever. since there are not intervals of energy levels.