# What Temperature is Needed for Hydrogen Gas to Produce a 656.2nm Emission Line?

• indie452
In summary, the question is asking for an approximation of the temperature needed for hydrogen gas to produce a line with a wavelength of 656.2nm in its emission spectrum. The energy difference between the electron levels involved is approximately 1.89ev. There are two potential ways to approach this question, either using the internal energy formula of 1/2(3RT) or Wien's law for black bodies. However, using 1/2(3RT) gives a temperature of 14637K, which seems too high compared to the temperature of the Sun (~5000K) where similar lines can be observed. This is because Wien's law is not applicable in this scenario. The estimated temperature for the gas using the internal
indie452
the question states that the emission spectrum of hydrogen contains a line with wavelength 656.2nm. and we need to approx find out what temp the H gas needs to have to be heated before this line appers in the spectrum

i have worked out that for this wavelength the electron mov from level 3 to 2, and that the energy between these two levels is ~1.89ev (3.03E-19 J)

im not sure whether i can use the internal energy formula = 1/2(RfnT) = 1/2(3RT)
or the weins law for blackbodies => lamda = 2.898E-3/T

If you are looking for an aproximation (oder of magnitude) you can just use kBT for average thermal energy per molecule.
kB is Boltzmann constant.

indie452 said:
im not sure whether i can use the internal energy formula = 1/2(RfnT) = 1/2(3RT)
or the weins law for blackbodies => lamda = 2.898E-3/T

I don't know how you plan to use lamda = 2.898E-3/T, but you can certainly use 1/2(3RT). 1/2(3RT) is the internal energy that each mole of gas has; 1/2(3kT) is the internal energy of each molecule.

but if i use 1/2(3kT) i get for the temp = 14637K this seems too big as H-alpha lines can be seen in the sun and that has a temp of ~5000K which is about 3 times smaller, but if i use 2.898E-3/T i get 4416K which seems more reasonable, but i would have thought the first way would give a reasonable answer. if it i correct then what does the 14637K represent?

Wien's law is for a black body radiation. It does not really apply to the question you have here.

The question is about just an estimate of the order of magnitude. It does not really matter if you take the factor 3/2 in front of the energy. That energy is the AVERAGE thermal energy.
Even at lower temperatures when the average is lower, there are molecules with higher energies that can excite the line considered.
So you get something like 10,000 K. The Sun has 6000 K. Is the same order of magnitude.
That's all you can expect from this estimate. For more accurate calculation you need to look at the actual distribution of the energies and define what exactly is required to observe the line in the spectrum.

## What is the emission spectrum of hydrogen?

The emission spectrum of hydrogen refers to the specific wavelengths of light that are emitted when an electron in a hydrogen atom transitions from a higher energy level to a lower one. This produces a unique pattern of spectral lines that can be observed using a spectroscope.

## Why is the emission spectrum of hydrogen important?

The emission spectrum of hydrogen is important because it provides valuable information about the energy levels of the atom and the behavior of its electrons. This can help scientists understand the structure of atoms and how they interact with each other.

## How is the emission spectrum of hydrogen produced?

The emission spectrum of hydrogen is produced when energy, such as heat or electricity, is applied to a sample of hydrogen gas. This causes the electrons in the atoms to move to higher energy levels, and when they return to their original energy level, they release energy in the form of light.

## What is the significance of the Balmer series in the emission spectrum of hydrogen?

The Balmer series is a specific set of spectral lines in the emission spectrum of hydrogen that correspond to the electron transitioning from the third energy level to the second energy level. This series was one of the first pieces of evidence for the existence of quantized energy levels in atoms and helped to develop the concept of quantum mechanics.

## How does the emission spectrum of hydrogen relate to the Bohr model of the atom?

The emission spectrum of hydrogen is closely related to the Bohr model of the atom. The model explains how the electrons in a hydrogen atom are arranged in discrete energy levels, and the emission spectrum shows the specific energies of light that are released when these electrons move between levels. This helped to support the idea of quantized energy levels in atoms proposed by the Bohr model.

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