4. The wavelength of electromagnetic radiation that is given off when an electron returns from n=2 to the ground state (n=1) is __ nm.

Here's how to calculate the wavelength:**1. Understand the concept:**The electron transition from a higher energy level (n=2) to a lower energy level (n=1) releases energy in the form of electromagnetic radiation. The energy of this radiation is equal to the difference in energy between the two levels. We can use the Rydberg formula to calculate this energy difference and then relate it to the wavelength.**2. Rydberg Formula:**The Rydberg formula for hydrogen-like atoms is:1/λ = R * Z² * (1/n₁² - 1/n₂²)Where:* λ is the wavelength of the emitted radiation* R is the Rydberg constant (approximately 1.097 x 10⁷ m⁻¹)* Z is the atomic number (for hydrogen, Z = 1)* n₁ is the principal quantum number of the lower energy level (n=1 in this case)* n₂ is the principal quantum number of the higher energy level (n=2 in this case)**3. Calculation:**1/λ = (1.097 x 10⁷ m⁻¹) * 1² * (1/1² - 1/2²)1/λ = (1.097 x 10⁷ m⁻¹) * (1 - 1/4)1/λ = (1.097 x 10⁷ m⁻¹) * (3/4)1/λ = 8.2275 x 10⁶ m⁻¹λ = 1 / (8.2275 x 10⁶ m⁻¹)λ ≈ 1.215 x 10⁻⁷ m**4. Convert to nanometers:**Since 1 meter = 1 x 10⁹ nanometers:λ ≈ 1.215 x 10⁻⁷ m * (1 x 10⁹ nm/m)λ ≈ 121.5 nm**Answer:** 121.5 nm