what is the wavenumber and wavelength of the first transition in lyman Balmer paschen series in atomic spectra of hydrogen
Answers
the ritz-combination equation also called as rydbergs equation is the concept
the equation is used in calculating the wave length,frequency and wave number.
\frac{1}{\lambda_{vac}} = R_\infty \left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)
Where
\lambda_{vac} \! is the wavelength of electromagnetic radiation emitted in vacuum,
R_\infty \! is the Rydberg constant, approximately 1.097 * 107 m-1,
n_1\! and n_2\! are integers such that n_1 < n_2\!.
By setting n1 to 1 and letting n2 run from 2 to infinity, the spectral lines known as the Lyman series converging to 91 nm are obtained, in the same manner:
n1 n2 Name Converge toward
1 2 → ∞ Lyman series ??91.13 nm (UV)
2 3 → ∞ Balmer series ?364.51 nm (Visible)
3 4 → ∞ Paschen series ?820.14 nm (IR)
4 5 → ∞ Brackett series 1458.03 nm (IR)
5 6 → ∞ Pfund series 2278.17 nm (IR)
6 7 → ∞ Humphreys series
3280.56 nm (IR)
this is the concept
we know that wavenumber of lyman series is given by 109677(1/1² -1/n₂²)cm⁻¹
the first transition of lyman series is from n₁ = 1 to n₂ = 2
⇒ wavenumber of lyman series is 109677(1 - 1/2²)
= 109677 × 0.75 = 82257.75cm⁻¹
we know that wavenumber is the reciprocal of wavelength.
⇒ wavelength of lyman series = 1/82257.75 = 1.21 × 10⁻⁵ cm = 1.21 × 10⁻⁷ m.
we know that wavenumber of balmer series is given by 109677(1/2² -1/n₂²)cm⁻¹
the first transition of balmer series is from n₁ = 2 to n₂ = 3
⇒ wavenumber of balmer series is 109677(1/2² - 1/3²)
= 109677 ×(1/4 - 1/9) = 15232.91 cm⁻¹
we know that wavenumber is the reciprocal of wavelength.
⇒ wavelength of balmer series = 1/15232.91 = 6.56 × 10⁻⁵ cm = 6.56 × 10⁻⁷ m.
we know that wavenumber of pashen series is given by 109677(1/3² -1/n₂²)cm⁻¹
the first transition of pashen series is from n₁ = 3 to n₂ = 4
⇒ wavenumber of pashen series is 109677(1/3² - 1/4²)
= 109677 ×(1/9 - 1/16) = 5331.520 cm⁻¹
we know that wavenumber is the reciprocal of wavelength.
⇒ wavelength of pashen series = 1/5331.520 = 1.87 × 10⁻⁴ cm = 1.87 × 10⁻⁶ m.