Hydrogen atoms absorb energy so that the electrons are excited to the energy lev

Question

Hydrogen atoms absorb energy so that the electrons are excited to the energy level n = 7. Electrons then undergo these transitions: n = 7 rightarrow n = 1 n = 7 rightarrow n = 6 n = 2 rightarrow n = 1 which transition will produce the photon with the smallest energy?(enter the letter of the correct answer, e.g. C) ______What is the frequency of a photon resulting from the transition of n = 6 rightarrow n = 1?(give answer to 3 digits) 8.39 times 10^14 1.05 times 10^15 1.31 times 10^15 1.64 times 10^15 2.05 times 10^15 2.56 times 10^15 3.20 times 10^15 4.00 times 10^15

Explanation / Answer

Lets use following formula

Delta E = k( 1/ni^2 - 1/nf^2 )

The value of bracket decide the magnitude of energy.

If n=7 to n=6 , then the value of bracket is lowest so the energy value for this will be lowest.

So answer is B. n=7 to n=6

Part II

Calculation of frequency

Frequency = E/h

Here E is in Joule , h is planks constant.

Lets calculate energy

E = 2.18 E-18 ( 1/ni^2 - 1/nf^2 )

Lets plug in the values

E = 2.18 E-18 (1/6^2 - 1/ 1^2)

E = -2.119 E-18 J

Frequency = 2.119 E-18 / 6.626 E-34

= 3.20 x 10^15 Hz

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