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The Rydberg-Ritz equation describes the wavelengths of photons absorbed or emitted when electrons in the hydrogen atom undergo transitions between a lower energy level, nl and an upper energy level nu.If nl = 2 and nu= 6, what is the wavelength of a photon that is absorbed or emitted when an electron undergoes a transition between these states?Express answer in nanometres, rounded to the nearest whole number.

Question

The Rydberg-Ritz equation describes the wavelengths of photons absorbed or emitted when electrons in the hydrogen atom undergo transitions between a lower energy level, nl and an upper energy level nu.If nl = 2 and nu= 6, what is the wavelength of a photon that is absorbed or emitted when an electron undergoes a transition between these states?Express answer in nanometres, rounded to the nearest whole number.

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Solution

The Rydberg-Ritz equation is given by:

1/λ = R * (1/nl^2 - 1/nu^2)

where R is the Rydberg constant, λ is the wavelength, nl is the lower energy level, and nu is the upper energy level. The Rydberg constant R is approximately 1.097373 x 10^7 m^-1.

Substituting the given values into the equation:

1/λ = 1.097373 x 10^7 * (1/2^2 - 1/6^2)

Solving the equation gives:

1/λ = 1.097373 x 10^7 * (1/4 - 1/36)

1/λ = 1.097373 x 10^7 * (9 - 1)/36

1/λ = 1.097373 x 10^7 * 8/36

1/λ = 2.43871 x 10^6 m^-1

Therefore, λ = 1 / 2.43871 x 10^6 = 4.10 x 10^-7 m

Converting to nanometers (1 m = 10^9 nm), we get:

λ = 4.10 x 10^-7 * 10^9 = 410 nm

Rounding to the nearest whole number, the wavelength of a photon that is absorbed or emitted when an electron undergoes a transition between these states is approximately 410 nm.

This problem has been solved

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