Question

Calculate the shortest and the longest wavelengths of the Lyman series. Given Rydberg constant=10967700 1\m

Answer 1

Answer:

Shortest = 911.75 Å, Longest = 1215.67 Å

Explanation:

Rh = 10967700 m⁻¹ ⇒ 109678 cm⁻¹

1/λ = Rh [1/n₁² + 1/n₂²]

In Lyman series n₁ = 1 and for shortest wavelength energy difference in transitional states will be maximum. So n₂ = ∞

1/λ = 109678 [1/1² - 1/∞²]

1/λ = 109678 [1+0]

λ = 1/109678

λ = 9.117598x10⁻⁶ cm

λ = 911.75Å    

for the longest wavelength energy difference will be minimum. So n₂ = 2

1/λ = 109678 [1/1² - 1/2²]

1/λ = 109678 (3/4)

λ = 4/(3x109678)

λ = 12.1567x10⁻⁶ cm

λ = 1215.67Å

Answer 2

Answer:

Shortest = 911.75 Å, Longest = 1215.67 Å

Explanation:

Rh = 10967700 m⁻¹ ⇒ 109678 cm⁻¹

1/λ = Rh [1/n₁² + 1/n₂²]

In Lyman series n₁ = 1 and for shortest wavelength energy difference in transitional states will be maximum. So n₂ = ∞

1/λ = 109678 [1/1² - 1/∞²]

1/λ = 109678 [1+0]

λ = 1/109678

λ = 9.117598x10⁻⁶ cm

λ = 911.75Å    

for the longest wavelength energy difference will be minimum. So n₂ = 2

1/λ = 109678 [1/1² - 1/2²]

1/λ = 109678 (3/4)

λ = 4/(3x109678)

λ = 12.1567x10⁻⁶ cm

λ = 1215.67Å

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