Spectral lines
All elements have a unique electromagnetic signature.
We will discuss the visible portion, of the electromagnetic spectrum.
Elements absorb or emit photons in a unique fashion.
This helps us to identify elements, even if the light is coming from a sun,
or a distant star.
In quantum theory and in the Bohr's model,
the electron cloud, orbits the nuclei.
The electrons have well defined orbitals.
These orbitals are quantised.
The orbitals are defined by the principle quantum number.
This can take the values of 1, 2, 3, 4, 5, 6, etc.
Each orbital has a definitive energy level,
for each element.
In this discussion, we will use hydrogen, as an example to understand,
spectral lines.
Hydrogen has one electron.
In its normal or ground state, the electron will occupy the first orbital.
The first orbital or the ground orbital, has the lowest energy.
Higher orbitals will have higher energy.
In the first orbital, principal quantum number 'n' will be equal to 1.
Its energy will be 'E' subscript 1 or 'E1'.
The hydrogen atom can be excited.
This can happen when it absorbs a photon.
A photon carries energy.
This can raise the electron from the first orbit,
to the second orbit.
This corresponds to the principal quantum number 2.
It would be worth while to note, that the electrons,
can move only from one orbital to the next,
and not somewhere in-between.
When the electron returns to the first orbit, it will emit a photon.
The energy of this photon will be fixed.
It will be the difference of the energy of the second and the first orbit.
This will be equal to 'E2' minus 'E1'.
Similarly when an electron jumps from level 3 to level 2,
it will emit a photon, with a specific energy.
Photon with a specific energy, will have a specific colour in the visible spectrum.
Electrons can also jump from energy levels 4, 5, 6 to energy levels 2.
It is convenient to discuss, electrons jumping to level 2,
because the emitted photons have energy levels corresponding to,
a colour in the visible spectrum.
When the electron jumps from energy level 3, to energy level 2,
it will emit light, in red colour.
This has a wave length of 656 nanometers.
When the electron jumps from energy level 4, to energy level 2,
it will emit light, in blue-green colour.
This has a wave length of 486 nanometers.
When the electrons jumps from energy level 5, to energy level 2,
it will emit light, in blue colour.
This has a wave length of 434 nanometers.
When the electrons jumps from energy level 6, to energy level 2,
it will emit light, in violet colour.
This has a wave length of 410 nanometers.
These colours can be captured using instruments called spectrometers.
The captured image will have a distinct,
red band, blue-green band, blue band and violet band.
These are called spectral lines.
This spectrogram is a distinct signature of the element hydrogen.
If we analyse the light from a distant star,
using a spectrometer.
We can detect the presence of hydrogen,
if it exhibits the spectral line signature, we just discussed.
We will now discuss the scientific basis of this phenomena.
The energy of a photon is equal to,
the Planck's constant, multiplied by the frequency of,
the photons wave length.
Planck's constant is denoted by the character 'h'.
Frequency is denoted by the greek character 'nu', or just 'f'.
We will use 'f' for frequency for convenience.
So, 'e' is equal to 'hf'.
There is a relationship between frequency and wave length of light.
Frequency is equal to 'c' divided by wave length.
'c' is the speed of light.
Wave length is denoted by the Greek letter lambda.
Let us take a general case of an electron jumping,
from a low level 'i', to a higher level 'j'.
The energy of the emitted photon,
will be 'EJ' minus 'Ei'.
So, 'EJ' minus 'Ei' is equal to 'h' multiplied by 'c',
divided by lambda.
The energy at any level, is given by the equation,
'E1' divided by 'n' squared.
'E1' is the energy in the ground state.
'n' is the principal quantum number.
So, the energy 'EJ' at level 'j' is equal to 'E1' by 'j' squared.
Energy 'Ei' at the level 'i' is equal to 'E1' by 'i' squared.
So, 'EJ' minus 'Ei' = 'E1' by 'j' squared, minus 'E1' by 'i' squared,
which is equal to 'h' into 'c' by lambda.
This equation can be rewritten as,
1 by lambda = 'E1' by 'hc',
open bracket, (1 by 'j' squared minus 1 by 'i' squared) close bracket.
The terms 'E1'by 'hc', are all constants.
If we substitute the values of 'E1', 'h', 'c',
we will get a constant value.
This is called as the Rydberg constant,
denoted by 'R'.
The value of 'E1' = minus 2.17 into 10 to the power of minus 18.
The value of Planck's constant 'h' is = 6.6626 into, 10 to the power of minus 34.
The value of the speed of light 'c' = 2.9779 into, 10 to the power of 8 meters per second.
The value of the Rydberg constant works out to 1.097 into 10 to the power of 7, 1 by meter.
The simplified equation becomes,
1 by lambda = 'R' open bracket, (1 by 'j' squared minus 1 by 'i' squared) close bracket.
This is called the Balmer Rydberg equation, or simply the Balmer series.
This equation gives the entire emission spectrum of hydrogen.
If we substitute the values for 'i' and 'j',
we can derive the wave length of the different spectral lines,
of the hydrogen spectrum.
This will turn out to be the same values of :
Red of 656 nanometers.
Blue-green of 486 nanometers.
Blue of 434 nanometers.
Violet of 410 nanometers.
This is the signature spectrum of hydrogen.
This can be detected from the light coming from the sun, and billions of stars.
This is how we know, that all stars have hydrogen.
For convenience we discuss the series of spectral lines generated,
when electrons jump from levels 6, 5, 4, 3, to level 2.
What happens when an electron jumps from level 2 to level 1?
1 by lambda =,
Open bracket (1 by 1 squared minus 1 by 2 squared) close bracket.
This works out to a wave length of 122 nano meters.
This wave length falls in the ultra violet range.
Similarly there will be other energy changes which fall in infrared range.
This wave length also is not in the visible spectrum.
This is the reason, we took the example of electrons,
dropping to the second energy level in hydrogen.
It is very much possible to measure wave lengths outside the visible spectrum,
using instruments.
Scientists do this routinely.
The principle remains the same,
whether the spectral lines are in the visible range,
or outside the visible range.
Scientists have established the different series for electrons,
jumping to different levels.
Electrons jumping from any level:
to level 1 is called the Lyman ultra violet series.
to level 2 is called the Balmer series.
to level 3 is called the infrared Paschen series.
to level 4 is called the Bracket series.
We had expressed the first energy level,
E1 as minus 2.17 into 10 to the power of minus 18 joules.
Energy can be expressed in electron volts or 'e v'.
1 electron volt or 'e v' = 1.6 into 10 to the power of minus 19 joules.
E1 = minus 13.6 electron volts or 'e v'.
This is the energy of an electron in the lowest energy level in hydrogen.
The energy in other levels is given by the formula,
E n = E1 by n squared.
Using this formula, we can work out the energy at different levels for hydrogen.
E1 = minus 13.6 'e v'.
E2 = minus 3.4 'e v'.
E3 = minus 1.5 'e v'.
All the energy levels are quantised in this manner.
We can easily calculate the energy, when the electron jumps between two levels.
For example, E2 minus E1 = minus 3.4 minus 13.6 = 12.4 'e v'.
E3 minus E1 = minus 13.6 minus 1.51 = 12.09 'e v'.
We can even calculate the energy required, to pull the electron,
to a large or infinite level.
In this case 'n' = infinity.
So, the energy E infinity minus E1 = minus 13.6 'e v'.
This effectively is the energy required to ionise, an
hydrogen atom to H+ ion.
Every thing in the universe glows with its own internal heat.
Heat is the energy of random particles, moving or jiggling with in the body.
The hotter the particle is the faster is the jiggling.
Accelerating charges in jiggling particles, produces electro magnetic radiation.
Hotter objects produce higher frequencies.
Human beings glow in infrared frequencies.
Using infrared glasses we can see humans and animals even in the dark.
All the elements in the universe were cooked in some stars,
by nuclear reactions.
Different stars have different composition of elements.
Sophisticated telescopes and instruments are now available,
to study the electromagnetic radiation from stars.
Scientists are able to study the composition of stars,
using spectrography.