Solved: Value of Infinity for Hydrogen Atom Wavelength

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In summary, the value of infinity is used to represent the shortest possible wavelength of light emitted by an electron in the Brackett series of spectra lines of the hydrogen atom. By substituting zero in place of infinity in the given equation, we can calculate the correct answer of 1.45 x 10^-6.
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alexlee33
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[SOLVED] Value of inifinity?

Edit: typo in title (infinity); sorry

Homework Statement



What is the shortest wavelength of light emitted by an electron in the Brackett series of spectra lines of the hydrogen atom?

Homework Equations



1 / (wavelength) = RH ( (1/nu^2) - (1/nl^2) )

The Attempt at a Solution



1 / (wavelength) = 1.1 x 10^7 ( (1/4^2) - (1/(infinity?)^2) )

I am told the correct answer is 1.45 x 10^-6, but I cannot find it on my calculator because I am not sure what to put in the place of infinity.

Thanks!
 
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  • #2
One over a number infinitely close to infinity is infinitely close to zero. Just put in zero for the second term.
 
  • #3
The value of 1/x tends to zero as x tends to infinity.So, just put zero in place of 1/n1^2.
 
  • #4
(Sorry Dick, it seems we were typing at almost the same time.)
 
  • #5
Thanks guys! :)
 

FAQ: Solved: Value of Infinity for Hydrogen Atom Wavelength

What is the value of infinity for hydrogen atom wavelength?

The value of infinity for hydrogen atom wavelength is not a concrete number that can be measured. It is a theoretical concept used in the mathematical equations that describe the energy levels and wavelengths of the electron in the hydrogen atom.

How is the value of infinity used in calculating the hydrogen atom wavelength?

The value of infinity is used in the formula for the energy levels of the electron in the hydrogen atom, known as the Rydberg formula. It represents the limit of the electron's energy as it approaches the nucleus. The energy level and corresponding wavelength for the electron are then determined by this value of infinity.

Is the value of infinity the same for all atoms?

No, the value of infinity for hydrogen atom wavelength is specific to the hydrogen atom and is not applicable to other atoms. Each element has its own unique set of energy levels and wavelengths, which are determined by the number of protons and electrons present.

Why is the value of infinity used in the calculations for the hydrogen atom?

The value of infinity is used in the calculations for the hydrogen atom because it represents the theoretical limit of the electron's energy as it approaches the nucleus. This helps to accurately describe the energy levels and wavelengths of the electron in the hydrogen atom, allowing for precise predictions and calculations in atomic physics.

Can the value of infinity for hydrogen atom wavelength be measured experimentally?

No, the value of infinity cannot be measured experimentally. It is a theoretical concept used in mathematical equations to describe the energy levels and wavelengths of the electron in the hydrogen atom. However, the effects of this value can be observed and measured through experiments such as spectroscopy, which studies the absorption and emission of light by atoms.

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