Question

Atomic hydrogen produces a well-known series of spectral lines in several regions of the electromagnetic spectrum. Each series fits the Rydberg equation with its own particular n1 value. Calculate the value of n1 that would produce a series of lines in which the highest energy line has a wavelength of 1459 nm.

Answer 1

Answer:

The value of n₁ is 3.9636

Explanation:

The Rydberg expression is:

$\frac{1}{\lambda } =\nu =(\frac{1}{n_{1}^{2} }-\frac{1}{n_{2}^{2} } )*R$

Here:

R=Rydberg constant=109678cm⁻¹

n₂=highest energy line=∞

λ=1459nm=1459x10⁻⁷cm

Replacing:

$\frac{1}{1459x10^{-7} } =(\frac{1}{n_{1}^{2} } -\frac{1}{\alpha } )*107678\\6854.0096=(\frac{1}{n_{1}^{2} } -0} )*107678\\0.0637=\frac{1}{n_{1}^{2}}\\n_{1} =3.9636$