Question

In some parts of the galaxy, electrons in hot hydrogen gas may be excited to very high quantum levels. Calculate the wavelength of light that would be emitted if electrons moved from the =20 shell to the =2 shell.

Answer 1

The wavelength of the light emitted when electrons move from the n=20 shell to the n=2 shell in a hydrogen atom is approximately 4.862 x 10^6 nm.

Step-by-step explanation:

When electrons move from one energy level to another in an atom, they emit or absorb light at specific wavelengths. The energy difference between the two levels determines the wavelength of the emitted or absorbed light. In this case, the electrons are moving from the n=20 shell to the n=2 shell in a hydrogen atom.

To calculate the wavelength of the light emitted, we can use the Rydberg equation, which relates the wavelength to the energy difference:

1/λ = R*(1/n1^2 - 1/n2^2)

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

Plugging in the values n1=20 and n2=2, we get:

1/λ = 1.097 x 10^7*(1/2^2 - 1/20^2)

Simplifying the equation gives:

λ ≈ 4.862 x 10^6 nm

Therefore, the wavelength of the light emitted when electrons move from the n=20 shell to the n=2 shell in a hydrogen atom is approximately 4.862 x 10^6 nm.