Respuesta :
Complete Question
The complete question is shown on the first uploaded image
Answer:
The value of n is [tex]n =7[/tex]
Explanation:
From the question we are told that
The value of m = 2
For every value of [tex]m, n = m+ 1, m+2,m+3,....[/tex]
The modified version of Balmer's formula is [tex]\frac{1}{\lambda} = R [\frac{1}{m^2} - \frac{1}{n^2} ][/tex]
The Rydberg constant has a value of [tex]R = 1.097 *10^{7} m^{-1}[/tex]
The objective of this solution is to obtain the value of n for which the wavelength of the Balmer series line is smaller than 400nm
For m = 2 and n =3
The wavelength is
[tex]\frac{1}{\lambda } = (1.097 * 10^7)[\frac{1}{2^2} - \frac{1}{3^2} ][/tex]
[tex]\lambda = \frac{1}{1523611.1112}[/tex]
[tex]\lambda = 656nm[/tex]
For m = 2 and n = 4
The wavelength is
[tex]\frac{1}{\lambda } = (1.097 * 10^7)[\frac{1}{2^2} - \frac{1}{4^2} ][/tex]
[tex]\lambda = \frac{1}{2056875}[/tex]
[tex]\lambda = 486nm[/tex]
For m = 2 and n = 5
The wavelength is
[tex]\frac{1}{\lambda } = (1.097 * 10^7)[\frac{1}{2^2} - \frac{1}{5^2} ][/tex]
[tex]\lambda = \frac{1}{2303700}[/tex]
[tex]\lambda = 434nm[/tex]
For m = 2 and n = 6
The wavelength is
[tex]\frac{1}{\lambda } = (1.097 * 10^7)[\frac{1}{2^2} - \frac{1}{6^2} ][/tex]
[tex]\lambda = \frac{1}{2422222}[/tex]
[tex]\lambda = 410nm[/tex]
For m = 2 and n = 7
The wavelength is
[tex]\frac{1}{\lambda } = (1.097 * 10^7)[\frac{1}{2^2} - \frac{1}{7^2} ][/tex]
[tex]\lambda = \frac{1}{2518622}[/tex]
[tex]\lambda = 397nm[/tex]
So the value of n is 7
