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Scientists have found interstellar hydrogen atoms with quantum number n in the hundreds. calculate the wavelength of light emitted when a hydrogen atom undergoes a transition from n = 236 to n = 235. in what region of the electromagnetic spectrum does this wavelength fall? a) Ultraviolet

b) Infrared
c) X-ray
d) Radio waves

1 Answer

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Final answer:

The wavelength of light emitted during the transition from n = 236 to n = 235 for a hydrogen atom is approximately 1898 nm, which falls into the infrared region of the electromagnetic spectrum.

Step-by-step explanation:

To calculate the wavelength of light emitted when a hydrogen atom undergoes a transition from n = 236 to n = 235, we use the Rydberg formula for the hydrogen emission spectrum:

\(\frac{1}{\lambda} = R \left( \frac{1}{{n_f}^2} - \frac{1}{{n_i}^2} \right)\)

where:

  • \(\lambda\) is the wavelength of the emitted light,
  • \(R\) is the Rydberg constant (\(1.097 \times 10^7 m^{-1}\)),
  • \(n_i\) is the initial energy level (236),
  • \(n_f\) is the final energy level (235).

Plugging in the values, we get:

\(\frac{1}{\lambda} = 1.097 \times 10^7 m^{-1} \left( \frac{1}{235^2} - \frac{1}{236^2} \right)\)

After calculating, we find:

\(\lambda \approx 1.898 \times 10^{-3} m\)

or

\(\lambda \approx 1898 nm\) which falls into the infrared region of the electromagnetic spectrum.

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