Question

The wavelength of the first line of the Balmer spectrum of hydrogen will be.
A. ${{4340A}}^\circ$
B. ${{4101}}{{{A}}^{{o}}}$
C. ${{6569}}{{{A}}^{{o}}}$
D. ${{4861}}{{{A}}^{{o}}}$

Answer 1

We know The Balmer arrangement, or Balmer lines in nuclear material science, is one of a bunch of six named arrangements depicting the otherworldly line discharges of the hydrogen iota. The Balmer arrangement is determined utilizing the Balmer recipe, an exact condition found by Johann Balmer in $1885$ .

Complete step by step answer:
Balmer $\Rightarrow {n_1} = 2$
Hydrogen $\Rightarrow Z = 1$
$\dfrac{{{1}}}{{{\lambda }}}{{ = R}}{\left( {{1}} \right)^{{2}}}\left[ {\dfrac{{{1}}}{{{{{2}}^{{2}}}}}{{ - }}\dfrac{{{1}}}{{{{{n}}^{{2}}}}}} \right]$ from Rydberg's equation
First line of Balmer series is form n=3
$\dfrac{{{1}}}{{{\lambda }}}{{ = 10967800}}\left( {{1}} \right)\left[ {\dfrac{{{1}}}{{{{{2}}^{{2}}}}}{{ - }}\dfrac{{{1}}}{{{{{3}}^{{2}}}}}} \right]$
On simplification we get,
${{\lambda = 6569}}{{{A}}^{{o}}}$

So, the correct answer is Option c.

Additional information:
The obvious range of light from hydrogen shows four frequencies, 410nm,434nm,486nm & 656nm , that relate to discharges of photons by electrons in energized states changing to the quantum level portrayed by the essential quantum number n approaches. There are a few unmistakable bright Balmer lines with frequencies more limited than $400nm$. The quantity of these lines is an endless continuum as it moves toward a constraint of $364.6nm$ in the bright.

Note: We need to know that this arrangement of the hydrogen emanation range is known as the Balmer arrangement. This is the lone arrangement of lines in the electromagnetic range that lies in the noticeable district. The worth, $109,677c{m^{ - 1}}$ , is known as the Rydberg steady for hydrogen. The Balmer arrangement is fundamentally the piece of the hydrogen emanation range answerable for the excitation of an electron from the subsequent shell to some other shell. Additionally, different changes likewise have their own arrangement names. Some of them are recorded underneath,
Progress from the primary shell to some other shell – Lyman arrangement
Progress from the subsequent shell to some other shell – Balmer arrangement
Change from the third shell to some other shell – Paschen arrangement
Progress from the fourth shell to some other shell – Bracket arrangement
Change from the fifth shell to some other shell – Pfund arrangement.