Chapter 37: Q. 3 (page 1081)

The wavelengths in the hydrogen spectrum with $m = 1$ form a series of spectral lines called the Lyman series. Calculate the wavelengths of the first four members of the Lyman series.

Short Answer

Expert verified

The wavelengths of the first four members of the Lyman series are :

For $n = 2$ ; $λ = 121.57 n m$

For $n = 3$ ; $λ = 102.57 n m$

For $n = 4$ ; $λ = 97.26 n m$

For $n = 5$ ; $λ = 94.98 n m$

Step by step solution

Given information

We need to find the wavelengths of the first four members of the Lyman series.

Simplify

The expression for the Lyman series is:

$λ = \frac{91.158 (n m)}{1 - \frac{1}{n^{2}}}$ , where ( $n = 2, 3, 4, . . .$ ) (Let this equation be (1) )

Here, $λ$ is the wavelength of the electron emitted and $n$ is the principle quantum number of the shell.

For $n = 2$ :

$λ = \frac{91.158 (n m)}{1 - \frac{1}{{(2)}^{2}}}$ (By substituting $n = 2$ in equation ( $1$ ))

$λ = 121.57 n m$

For $n = 3$ :

$λ = \frac{91.158 (n m)}{1 - \frac{1}{{(3)}^{2}}}$ (By substituting $n = 3$ in equation ( $1$ ))

$λ = 102.57 n m$

For $n = 4$ :

$λ = \frac{91.158 (n m)}{1 - \frac{1}{{(4)}^{2}}}$ (By substituting $n = 4$ in equation ( $1$ ))

$λ = 97.26 n m$

For $n = 5$ :

$λ = \frac{91.158 (n m)}{1 - \frac{1}{{(5)}^{2}}}$ (By substituting $n = 5$ in equation ( $1$ ))

$λ = 94.98 n m$

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The wavelengths in the hydrogen spectrum with $m = 1$ form a series of spectral lines called the Lyman series. Calculate the wavelengths of the first four members of the Lyman series.

Short Answer

Step by step solution

Given information

Simplify

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The wavelengths in the hydrogen spectrum with m=1form a series of spectral lines called the Lyman series. Calculate the wavelengths of the first four members of the Lyman series.

Short Answer

Step by step solution

Given information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Modern Physics

Force

Classical Mechanics

Physical Quantities And Units

Energy Physics

Famous Physicists

Study anywhere. Anytime. Across all devices.

The wavelengths in the hydrogen spectrum with $m = 1$ form a series of spectral lines called the Lyman series. Calculate the wavelengths of the first four members of the Lyman series.