Question

λ for one line of the hydrogen spectrum is .4118 x 10⁻⁴ cm. Use this value in the Rydberg equation to calculate the Rₕ value using n₁ = 2, and n₂ = 4.

Answer 1

To calculate the value of Rₕ using the Rydberg equation, we can use the given wavelength of λ = 0.4118 x 10⁻⁴ cm and the values of n₁ = 2 and n₂ = 4. Plugging in the values and solving the equation, we find that Rₕ = 4.056 x 10³ cm⁻¹.

Step-by-step explanation:

To calculate the value of Rₕ using the Rydberg equation, we can use the given wavelength of λ = 0.4118 x 10⁻⁴ cm and the values of n₁ = 2 and n₂ = 4. The Rydberg equation for the hydrogen spectrum is given by 1/λ = Rₕ(1/n₁² - 1/n₂²), where Rₕ is the Rydberg constant for hydrogen. Plugging in the values, we get:

1/0.4118 x 10⁻⁴ = Rₕ(1/2² - 1/4²)

Solving for Rₕ, we find:

Rₕ = (1/0.4118 x 10⁻⁴)/(1/4 - 1/16) = 4.056 x 10³ cm⁻¹.