Question

N the balmer-rydberg equation, what value of m is used to determine the wavelengths of the balmer series? express your answer as an integer.

Answer 1

Answer: n is equal to 2 m is an integer such that m > n.

Answer 2

The value of m is used to determine the wavelengths of the balmer series is 2.

Further Explanation:

Johann Jakob Balmer was born in Lausen, Switzerland on 1 May 1850 and he died in 12 March 1898. He was a Swiss mathematician and mathematical physicist.  

In an atomic physics the Balmer series is also called as Balmer lines and is calculated by using the Balmer formula. It is an empirical equations discovered by Johann Jakob Balmer in 1885. The Balmer series is set of six series explaining the spectral line emissions of the hydrogen atom.

Concept:

The Balmer series is used to find the wave length of the energy absorption or emission lines.

The expression for the wavelength can be expressed as follows:

$\fbox{\begin\\\lambda=B\left( {\dfrac{{{n^2}}}{{{n^2}-{m^2}}}} \right)\end{minispace}}$

Here, $\lambda$ is the wavelength, $B$ is the constant, $n$ and $m$ is the internes corresponding to the principle quantum numbers.

The value of B is $364.50682\text{ nm}$.

Johann Jakob Balmer did an experiment and observed that a single wavelength of $364.50682\text{ nm}$ has a relation to each line in the hydrogen spectrum that was in the visible light area. In the expression when any integer greater than $2$ for $n$, $2$ for $m$ and $364.50682\text{ nm}$ for $B$ is substitutes it gave the wavelength of the another line in the hydrogen spectrum which was not yet observed.

The physicist Johannes Rydberg in 1888 generalized the mathematical physicist Johann Jakob Balmer equations for all transitions of hydrogen and rearrange the expression. He wrote the expression just reciprocal rearrangement of the Balmer series. This expression is known as the Balmer-Rydberg equation.

The expression for the Balmer-Rydberg equation for wavelength can be expressed as follows:

$\fbox{\begin\\\dfrac{1}{\lambda }={R_H}\left( {\dfrac{1}{{{m^2}}} -\frac{1}{{{n^2}}}}\right)\end{minispace}}$

Here,${R_H}$ is the Rydberg constant and expressed as:

${R_H}=\dfrac{4}{B}$

The value of the Rydberg constant is $1.0968 \times {10^7}{\text{}}{{\text{m}}^{ - 1}}$.

Therefore, the value of m is used to determine the wavelengths of the balmer series is $2$.

Learn more:

1. Balmer series https://brainly.in/question/11701195

2. Balmer series formed brainly.com/question/12982733

3. Minimum wavelength of Lyman and Balmer series

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Answer Details:

Grade: High school

Subject: Physics

Chapter: Wave Nature  

Keywords:

Balmer-Rydberg equation, wavelength, Balmer series.