Please confirm Hydrogen atom question

[pinnacleprouk]

Homework Statement

Diagram not to scale:
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy (J)

n = 3 ----------------------------------------… - 0.24x10^-16
n = 2 ----------------------------------------… - 0.54x10^-18
n = 1 ----------------------------------------… - 2.18x10^-18

In which level is the electron to be found in a normal hydrogen atom? (need help with this question)

If the electron is promoted to the second excited state, (n=3), calculate the wavelengths of the photons which may be emitted?

(Planck's constant, h - 6.6x10^-34 Js c = 3.0x10^8 ms^-1)

Any help is greatly appreciated

Homework Equations

ΔE = hf

λ = c/v

h = 6.6x10^-34

c = 3.0x10^8

The Attempt at a Solution

n = 2 = - 0.54x10^-18
n = 3 = - 0.24x10^-16
ΔE = - 2.54x10^-17

ΔE = hf = - 2.54x10^-17 = 6.6x10^-34f

f = - 2.54x10^-17/6.6x10^-34 = -3.71x10^16 Hz

λ = c/v

λ = 3.0x10^8/- 3.71x10^16

λ = - 8.09x10^-9

See I know it's wrong as I end up with a negative value

Could you please point me in the right direction and explain the steps that are wrong please

 

[kuruman]

First the negative sign. Photon energies are always positive. The negative sign applies to the energy change of the emitting atom. If ΔE is positive/negative the atom gains/loses the energy that is carried by the absorbed/emitted photon.

The energies that you calculated for the first three level do not look correct. If you think they are, please show exactly how you got them.

Finally, to answer this question you need to consider all the possibilities of photon emission from the second excited state; they are more than one.

 

[pinnacleprouk]

Hi, thanks for the reply, the energies calculated for the first 3 energies are on the sheet given to me by the lecturer so not calculated by myself.

I assume they are not real world examples

 

[kuruman]

OK then. How many possibilities of emitted photons exist?

 

[graphene]

You can safely assume than the electron is in the ground state in a normal H atom.

For your next question, figure out in how many ways an electron in n = 3 can decay to a lower energy state.