What is the Correct Value of k for a 94.8 nm Photon Emission in Hydrogen?

[stickplot]

Homework Statement

The wavelength of the photon emitted when a hydrogen atom undergoes a transition from the k state to the n = 1 state is around 94.8 nm. How much is k?

Homework Equations

1/lambda= 1.97x10^7(1/1^2-1/k^2)

The Attempt at a Solution

1/9.48x10^-8=1.097x10^7(1-1/k^2)
10548523,71=1.097x10^7(1-1/k^2)
.9615791437=1-1/k^2
-.03384208563=-1/k^2
26.02753028=k^2
k=5.1 i thought it had to be an integer? do i just round off?

and I am also a bit confused because when i get the energy of transition= hc/lambda, it is equal to 1.31, but (energyK-energyN=energy of transition) .544-13.6= is not even close to 1.31 and i thought it was supposed to equal 1.31 (hf, energy transition) or is that only when the photon absorbs, :/ a bit confused help out please

 

[quantumdude]

Homework Statement

The wavelength of the photon emitted when a hydrogen atom undergoes a transition from the k state to the n = 1 state is around 94.8 nm. How much is k?

Homework Equations

1/lambda= 1.97x10^7(1/1^2-1/k^2)

The Attempt at a Solution

1/9.48x10^-8=1.097x10^7(1-1/k^2)
10548523,71=1.097x10^7(1-1/k^2)
.9615791437=1-1/k^2
-.03384208563=-1/k^2
26.02753028=k^2
k=5.1 i thought it had to be an integer? do i just round off?

Yes. $k=5$.

and I am also a bit confused because when i get the energy of transition= hc/lambda, it is equal to 1.31, but (energyK-energyN=energy of transition) .544-13.6= is not even close to 1.31 and i thought it was supposed to equal 1.31 (hf, energy transition) or is that only when the photon absorbs, :/ a bit confused help out please

You miscalculated. The transition energy is 13.1eV, not 1.31eV.

 

[stickplot]

o ok.
stupid me i see what i did now.
and btw
how do you know when a photon is absorbing energy?
is it when the photon energy is the same to the energy transition? but I am kind of confused because i thought they were always equal to each other