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Which transition emits photon of maximum frequency:1). 2nd spectral line of Balmer series 2). 2nd spectral line of Paschen series 3). 5th spectral line of Humphery series 4). 1st spectral line of Lumen series?
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Which transition emits photon of maximum frequency:1). 2nd spectral li...
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Introduction
In this question, we have to determine which transition emits photon of maximum frequency among the given options.

Spectral Series
Spectral series are the series of lines in the spectrum of an element. These lines are produced due to the emission of photons when an electron jumps from a higher energy level to a lower energy level.

Frequency of Photon
The frequency of a photon is given by the formula:

ν = E/h

where ν is the frequency of the photon, E is the energy of the photon, and h is the Planck's constant.

As we know, the energy of the photon emitted during a transition is given by:

ΔE = Ei - Ef

where ΔE is the energy of the photon, Ei is the energy of the initial state, and Ef is the energy of the final state.

Therefore, the frequency of the photon emitted during a transition is given by:

ν = (Ei - Ef)/h

Determination of Maximum Frequency
Now, we will determine which transition emits photon of maximum frequency among the given options.

1. 2nd spectral line of Balmer series
The second spectral line of Balmer series corresponds to the transition of an electron from the third energy level to the second energy level. The energy of the photon emitted during this transition is:

ΔE = E3 - E2

The frequency of the photon emitted during this transition is:

ν = (E3 - E2)/h

2. 2nd spectral line of Paschen series
The second spectral line of Paschen series corresponds to the transition of an electron from the fourth energy level to the third energy level. The energy of the photon emitted during this transition is:

ΔE = E4 - E3

The frequency of the photon emitted during this transition is:

ν = (E4 - E3)/h

3. 5th spectral line of Humphery series
The fifth spectral line of Humphery series corresponds to the transition of an electron from the seventh energy level to the fifth energy level. The energy of the photon emitted during this transition is:

ΔE = E7 - E5

The frequency of the photon emitted during this transition is:

ν = (E7 - E5)/h

4. 1st spectral line of Lumen series
The first spectral line of Lumen series corresponds to the transition of an electron from the second energy level to the first energy level. The energy of the photon emitted during this transition is:

ΔE = E2 - E1

The frequency of the photon emitted during this transition is:

ν = (E2 - E1)/h

Conclusion
We can see that the transition which emits photon of maximum frequency is the transition corresponding to the fifth spectral line of Humphery series, i.e., the transition of an electron from the seventh energy level to the fifth energy level.
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