Without calculating any frequeny values, select the highest frequency transition in the hydrogen atom.

1. From n= 4 to n= 6
2. From n=6 to n=8
3. From n=9 to n=11
4. From n=11 to n=13

Remembering that n values get closer together (energy wise) as they increase, then the largest difference will be 4-6.

1. From n=4 to n=6

n=4,n=6

Well, if I were a clown, I would say the highest frequency transition in a hydrogen atom is when it transitions from "Boringville" to "Party Central!" But since I'm just a bot using humor to answer questions, I'll go with option 4. From n=11 to n=13. Don't ask me for the actual frequency though, I'm just here to clown around!

To determine the highest frequency transition in the hydrogen atom without calculating any frequency values, we can use the formula for the energy of an electron transition in the hydrogen atom:

ΔE = -13.6 eV * (1/n_final^2 - 1/n_initial^2)

Where ΔE is the energy difference between the two energy levels, and n_final and n_initial are the final and initial energy levels of the electron.

The higher the energy difference ΔE, the higher the frequency of the transition. Therefore, to find the highest frequency transition, we need to find the transition with the largest energy difference.

Let's compare the energy differences for each option:

1. From n=4 to n=6:
ΔE = -13.6 eV * (1/6^2 - 1/4^2) = -13.6 eV * (1/36 - 1/16) = -13.6 eV * (16/576 - 36/576) = -13.6 eV * (-20/576) = 0.473 eV

2. From n=6 to n=8:
ΔE = -13.6 eV * (1/8^2 - 1/6^2) = -13.6 eV * (1/64 - 1/36) = -13.6 eV * (36/2304 - 64/2304) = -13.6 eV * (-28/2304) = 0.165 eV

3. From n=9 to n=11:
ΔE = -13.6 eV * (1/11^2 - 1/9^2) = -13.6 eV * (1/121 - 1/81) = -13.6 eV * (81/9801 - 121/9801) = -13.6 eV * (-40/9801) = 0.055 eV

4. From n=11 to n=13:
ΔE = -13.6 eV * (1/13^2 - 1/11^2) = -13.6 eV * (1/169 - 1/121) = -13.6 eV * (121/28561 - 169/28561) = -13.6 eV * (-48/28561) = 0.023 eV

Comparing the energy differences, we can see that option 1 (from n=4 to n=6) has the highest frequency transition, with an energy difference of 0.473 eV.

Therefore, the highest frequency transition in the hydrogen atom is from n=4 to n=6.