Question

For an advanced lab project, you are studying an unknown hydrogen-like atom. For these atoms, you determine that as excited atoms de-excite, the n = 3 → 2 transition emits a wavelength of 4.101 × 10⁻¸ m and the n = 4 → 2 transition emits a wavelength of 3.038 × 10⁻¸ m. Determine the wavelength (in m) of light emitted in the n = 4 → 3 transition.

Answer 1

To determine the wavelength of light emitted in the n = 4 -> 3 transition, we can use the formula for calculating the wavelength of electron transitions in a hydrogen-like atom.

Step-by-step explanation:

The wavelength of light emitted in the n = 4 -> 3 transition can be determined using the formula for calculating the wavelength of electron transitions in a hydrogen-like atom. The formula is given by:

λ = RH * [(1/nf2) - (1/ni2)]

where λ is the wavelength, RH is the Rydberg constant for hydrogen-like atoms, ni is the initial energy level, and nf is the final energy level.

Using the given information, we can substitute the values into the formula:

λ = RH * [(1/32) - (1/42)]

Calculating this equation will give us the wavelength of light emitted in the n = 4 -> 3 transition.