Chapter 5, Problem 99A

Interpretation Introduction

Interpretation:

In Bohr’s atomic model, electron-orbit transition that produces the blue-green line in hydrogen’s atomic emission spectrum needs to be identified.

Concept introduction:

Bohr proposed that electrons travel in circular orbits around the nucleus. An electron can jump between these orbits by absorbing or emitting a fixed amount of energy. The emission spectrum of atomic hydrogen has been divided into no. of spectral series according to lower energy state. Such as Lyman series, Balmer series, Paschen series and Fund series.

Answer to Problem 99A

The blue-green line in hydrogen atomic emission spectrum is produced when going from the  $n_{}=\text{ 4}$  down to the  $n_{}=2$.

Explanation of Solution

Lymen series includes lines emitted by transition of electrons from an outer orbit of quantum no. $n_2>1$ to the first orbit of principal quantum number $n_{1=}1$. These lines are in the $u-v$ region of spectrum of light.

The Balamer series includes lines that are emitted by the transition from an outer orbit $n_2>2$ to the orbit quantum number $n_1=2$. These lines are in the visible region of spectrum of light.

Other series like Paschen series and Fund series has lines that reside in the Infra Red region of the light spectrum. Now we know that which lines is visible part of light spectrum. So we can look for the blue green lines in Balmer series.

The range of wavelengths in the visible spectrum are the line with a wavelength of $410nm$ is violet in color, line with a wavelength of $434nm$ is blue in color, the one with a wavelength of $65nm$ is in the red region of the spectrum.

That leaves us with a line at $486nm$ which has a blue-green color and is a product of a transition from $n_2=4$ to $n_1=2$.

Conclusion

The blue-green line in hydrogen atomic emission spectrum is produced when going from the  $n_{}=\text{ 4}$  down to the  $n_{}=2$.