Question

Two of the wavelengths emitted by a hydrogen atorn are 102.6 nm and 1876 nm Part A What is the m value for the wavelength 102.6 nm ? Express your answer as an integer.

Answer 1

The m value for the wavelength 102.6 nm is 2.

Step-by-step explanation:

The m value refers to the principle quantum number, which represents the energy level or shell of an electron in an atom. In the case of hydrogen, the energy levels are determined by the formula:

En = -13.6eV / n2

Where n is the principle quantum number.

Since the wavelength of 102.6 nm corresponds to a visible light wavelength, it is part of the Balmer series. The Balmer series is given by the formula:

1/λ = R(1/22 - 1/n2)

For the wavelength of 102.6 nm, we can solve for n as follows:

1/λ = R(1/22 - 1/n2)

1/102.6 nm = R(1/4 - 1/n2)

Simplifying the equation, we get:

n2 - 4n + 2 = 0

Using the quadratic formula, we find that n = 2 (integer value) is the solution.