Question
Asked Nov 14, 2019
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25. Calculate the wavelengths, in nanometers, of the first
four lines of the Balmer series of the hydrogen spec-
trum, starting with the longest wavelength component.
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25. Calculate the wavelengths, in nanometers, of the first four lines of the Balmer series of the hydrogen spec- trum, starting with the longest wavelength component.

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Expert Answer

Step 1

Balmer Series: it is a one of a set of 6 named series describing the spectral line emissions of the H-atom. The balmer series is calculated using the balmer formula, an empirical equation discovered by Johann Balmer is 1885.

Rydberg Formula:

where
R Rydberg Constant
n, is constant, i.e., 2 andn,varies i.e.,n,-3,4,5,6
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where R Rydberg Constant n, is constant, i.e., 2 andn,varies i.e.,n,-3,4,5,6

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Step 2

For H – like particles, the formula is –

v =R
Z2
n2
---(ii)
or
C
R
109,677 cm or 1.097 x 10'm
Atomic number, for H-atom 1
Z
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v =R Z2 n2 ---(ii) or C R 109,677 cm or 1.097 x 10'm Atomic number, for H-atom 1 Z

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Step 3

Now we will calculate the wavelength of the balmer series of the hydrogen atom f...

z2
n
1
1.097 10 m
22 32
1
5
1.097 x 10 m
36
1
1.097 x 10 m1x 0.1388
1
0.1522636 x 10' m*
1
0.1522636 x 10
656.7 nm
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z2 n 1 1.097 10 m 22 32 1 5 1.097 x 10 m 36 1 1.097 x 10 m1x 0.1388 1 0.1522636 x 10' m* 1 0.1522636 x 10 656.7 nm

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