Question

Calculate the energy difference for a transition in the paschen series for a transition from the higher energy shell n=4. express your answer to four significant figures and include the appropriate units.

Answer 1

Electrons are orbiting around the nucleus in a specific energy level as described in Bohr's atomic model. There are 7 energy levels all in all; 1 being the strongest and nearest to the nucleus, and 7 being the weakest and farthest away from the nucleus. Electron can transfer from one energy level to another. If it increases energy, it absorbs energy. If it goes down an energy level, it emits energy in the form of light. This light can be measure in wavelength through the Rydberg equation:

1/λ =R(1/n₁² -1/n₂²), where
λ is the wavelength
R is the Rydberg constant equal to 1.097 × 10⁻7 per meter
n₁ and n₂ are the energy levels such that n₂>n₁

In the Paschen series is an emission spectrum of hydrogen when the energy level is at least n=4. So, this covers n=4 to n=7.

1/λ =(1.097 × 10⁻7)(1/4² -1/7²)
λ  = 216.57 ×10⁻⁶ m or 216.57 μm