# Calculation of no. of spectral lines for group of similar atoms

• Prabhu1
The question is how many lines do you get from 8 atoms, not from 1 atom.In summary, the maximum number of spectral lines for a single atom during its electron's transition is given by [∆n(∆n+1)]/2. However, when a group of atoms are present, the maximum number of spectral lines possible for the Balmer series is determined by the number of atoms in the group and the highest excited state of the atoms. In this specific problem, with 8 hydrogen atoms excited to the 6th excited state, there will be a total of 5 spectral lines for the Balmer series. This is because the equation only counts lines that end on n=2, and the
Prabhu1

## Homework Statement

The maximum no of spectral lines for a single atom during it's electron's transition is given by [∆n(∆n+1)]/2 . But I don't seem to arrive at the answer when a group of atoms are present . The question was - What is the maximum number of spectral lines possible for Balmer series when a set of 8 hydrogen atoms are irradiated with light and all are excited to 6th excited state and spectrum is obtained?
2. Homework Equations

[∆n(∆n+1)]/2

## The Attempt at a Solution

.[/B]
I am able to calculate the spectral lines for 1 atom which comes out to be 15 . But the answer key says 5 . i am not able to understand how .

Is that the exact full problem statement? If yes, I don't understand the given answer.

Also, be careful about the wording of the problem.. What is the 6th excited state?

mfb
DrClaude said:

Also, be careful about the wording of the problem.. What is the 6th excited state?
The 7th state

Prabhu1 said:
The 7th state
Correct. So how many Balmer series lines do you get?

DrClaude said:
Correct. So how many Balmer series lines do you get?
If we come down from each of the higher states directly like 7 ->2 , 6->2 and so on, we will get 5 lines , but there are still other ways to reach the 2nd state , aren't there?

Prabhu1 said:
but there are still other ways to reach the 2nd state , aren't there?
Like what?

DrClaude said:
Like what?
7 -> 6 ->2 .

Prabhu1 said:
7 -> 6 ->2 .
Wasn't that already taken care of who you wrote
Prabhu1 said:
If we come down from each of the higher states directly like 7 ->2 , 6->2 and so on, we will get 5 lines

In other words, where would the 6->2 come from if not from 7->6?

DrClaude said:
Wasn't that already taken care of who you wroteIn other words, where would the 6->2 come from if not from 7->6?
But still , we are getting a new spectral line for transition from 7 ->6 .

Prabhu1 said:
But still , we are getting a new spectral line for transition from 7 ->6 .
But that wouldn't be included in balmer series , right?

Prabhu1 said:
But still , we are getting a new spectral line for transition from 7 ->6 .
Is that line part of the Balmer series?

Prabhu1 said:
But that wouldn't be included in balmer series , right?
Our messages crossed. Yes, that's the point. You should only count the lines that end on n=2.

DrClaude said:
Our messages crossed. Yes, that's the point. You should only count the lines that end on n=2.
Okay , got you , silly mistake I did there .thank a ton sir . Btw I really liked your way of helping me , you didn't give out the answer straight away . thanks again .

Prabhu1 said:
Okay , got you , silly mistake I did there .thank a ton sir . Btw I really liked your way of helping me , you didn't give out the answer straight away . thanks again .
This is the way we do things here.

But aren't there 8 hydrogen atoms, that will make it 8X5=40

The atoms are all identical, they have identical spectral lines.

## 1. How is the number of spectral lines calculated for a group of similar atoms?

The number of spectral lines for a group of similar atoms can be calculated using the formula: n = nmax (nmax + 1) / 2, where n is the number of spectral lines and nmax is the maximum number of electrons in the outermost energy level of the atom.

## 2. What is the significance of calculating the number of spectral lines for a group of similar atoms?

Calculating the number of spectral lines allows us to understand the energy levels and transitions of electrons in an atom, which can provide valuable information about the atom's properties and behavior.

## 3. How does the number of spectral lines vary for different groups of atoms?

The number of spectral lines can vary for different groups of atoms based on their atomic structure and the number of electrons in their outermost energy level. For example, atoms with more electrons in their outermost energy level will have a higher maximum number of electrons, resulting in a larger number of spectral lines.

## 4. Can the number of spectral lines change for a single atom?

The number of spectral lines for a single atom remains constant, as it is determined by the atom's atomic structure. However, the intensity of the spectral lines can vary depending on the conditions under which the atom is observed.

## 5. How is the calculation of spectral lines used in scientific research?

The calculation of spectral lines is used in various scientific fields, including chemistry, physics, and astronomy, to analyze the properties and behavior of atoms. It can provide insights into atomic structure, energy levels, and electron transitions, which are essential for understanding chemical reactions, physical processes, and astronomical phenomena.

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