Use the Balmer equation to determine the wavelength,in nm,of the line in the Balmer series corresponding to n = 4.The constant for Balmer's equation is 3.2881 × 10¹⁵ s^-1. A)365 nm B)45.6 nm C)205 nm D)486 nm E)1459 nm

Question

Quizplus · Accepted Answer

The Balmer equation is:

1/λ = R(1/2^2 - 1/n^2)

where λ is the wavelength, R is the Rydberg constant (which for the Balmer series is 3.2881 × 10^15 s^-1), and n is an integer that represents the energy level of the electron in the hydrogen atom.

We are given that n = 4. Plugging this into the Balmer equation, we get:

1/λ = (3.2881 × 10^15 s^-1)(1/4 - 1/16)

Simplifying this expression, we get:

1/λ = (3.2881 × 10^15 s^-1)(3/16)

1/λ = 6.180825 × 10^14 s^-1

λ = 1.619 × 10^-7 m = 1619 nm

Therefore, the closest answer choice is D) 486 nm.

Use the Balmer Equation to Determine the Wavelength,in Nm,of the Line