# Electron falling between two orbits produces certain wavelenght of light

• Nano
In summary, to produce light of wavelength 954.8 nm, an electron in the Bohr hydrogen atom must fall from the n=3 to n=2 orbit. This can be calculated using the Rydberg formula and solving for the two energy levels.
Nano

## Homework Statement

Between which two orbits of the Bohr hydrogen atom must an electron fall to produce light of wavelength 954.8 nm ?

## Homework Equations

E = hv
E = R(1/n1^2 - 1/n2^2)

## The Attempt at a Solution

I've got it down to the differences in the reciprocals of the squares of the energy levels = .09548. I don't know how to calculate each n though. I've tried randomly plugging in different n's to see if i get .09548, but that's not getting me anywhere.

Any help would be great!

Hi there,

To calculate the two orbits between which the electron must fall, we can use the Rydberg formula:

1/λ = R(1/n1^2 - 1/n2^2)

Where λ is the wavelength of the emitted light, R is the Rydberg constant (1.097 x 10^7 m^-1), and n1 and n2 are the initial and final energy levels of the electron, respectively.

Solving for n1 and n2, we get:

n1 = sqrt(R/(1/λ + 1/n2^2))

n2 = sqrt(R/(1/λ - 1/n1^2))

Plugging in the given wavelength of 954.8 nm, we get:

n1 = sqrt(1.097 x 10^7 m^-1/(1/954.8 x 10^-9 m + 1/n2^2))

n2 = sqrt(1.097 x 10^7 m^-1/(1/954.8 x 10^-9 m - 1/n1^2))

To find the two orbits, we can try different values of n1 and n2 and see which combination gives us a difference of 0.09548. For example, if we let n1 = 2 and n2 = 3, we get a difference of 0.09548, meaning the electron must fall from the n=3 to n=2 orbit to produce light of wavelength 954.8 nm.

I hope this helps! Let me know if you have any further questions.

## 1. What is the significance of an electron falling between two orbits?

When an electron falls from a higher energy level to a lower one, it releases energy in the form of light. This phenomenon is known as emission spectrum and provides insight into the atomic structure and behavior of elements.

## 2. How does the distance between the orbits affect the wavelength of light produced?

The distance between the orbits determines the amount of energy released by the electron. The larger the distance, the higher the energy and thus, the shorter the wavelength of light produced.

## 3. Why does an electron fall between two orbits in the first place?

Electrons are constantly moving in an atom, and they can only occupy specific energy levels or orbits. When an external force, such as heat or light, is applied, it can cause the electron to move to a higher energy level. However, the electron will eventually fall back to its original energy level, releasing energy in the form of light.

## 4. Can an electron fall between any two orbits?

No, an electron can only fall between specific energy levels or orbits. The energy difference between the two orbits must match the energy of the emitted light for it to occur. This is why each element has a unique emission spectrum.

## 5. How is the wavelength of light produced by an electron falling between two orbits measured?

The wavelength of light can be measured using a spectroscope, which separates the different wavelengths of light emitted by an element. The resulting spectrum can then be compared to known spectra to determine the element present.

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