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Calculate the wavenumber for the longest wavelength transition in the Balmerseries of atomic hydrogen.

Question

Calculate the wavenumber for the longest wavelength transition in the Balmerseries of atomic hydrogen.

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Solution

Sure, to calculate the wavenumber for the longest wavelength transition in the Balmer series of atomic hydrogen, we need to use the Rydberg formula for hydrogen:

1/λ = R * (1/n1² - 1/n2²)

The Balmer series corresponds to the electron transitions from higher energy levels to the second energy level (n1=2). The longest wavelength transition in the Balmer series corresponds to the transition from the third energy level to the second (n2=3).

Substituting these values into the Rydberg formula, we get:

1/λ = R * (1/2² - 1/3²)

Solving this equation will give us the wavelength λ.

To convert this to wavenumber (ν), we use the relation ν = 1/λ.

So, the wavenumber for the longest wavelength transition in the Balmer series of atomic hydrogen can be calculated using these steps.

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