Question

Im not sure if Im right and this is my last attempt to check my answer. Please help!!

Be sure to answer all parts. Determine which of the following H atom electron transitions has the longest wavelength and which has the shortest wavelength: (a) =1 to n = 4 points (Ф) - 4 ton- 8 (c) = 4 ton= 9 eBook (d) n=1 to n = 12 Print References Longest-wavelength photon: оооо. Shortest-wavelength photon: 1 2 оооо е

Answer 1

Using Rydberg formula:

1/λ = R× Z²(1/n₁² - 1/n₂²)
where

λ = wavelength of the photon
R = Rydberg's constant (1.097 x 10⁷ m^-1)
Z = atomic number of the atom = For hydrogen,Z = 1
n₁ and n₂ are integers to denote orbits where n₂ > n₁

(a) n₁ = 1 , n₂ = 4

1/λ = 1.097 × 10⁷ × ( 1/1² - 1/4²)

λ = 9.72 × 10^-8 m

(b) n₁ = 4 , n₂ = 8

1/λ = 1.097 × 10⁷ × ( 1/4² - 1/8²)

λ = 1.94 × 10^-6 m

(c) n₁ = 4 , n₂ = 9

1/λ = 1.097 × 10⁷ × ( 1/4² - 1/9²)

λ = 1.81 × 10^-6 m

(d) n₁ = 1 , n₂ = 12

1/λ = 1.097 × 10⁷ × ( 1/1² - 1/12²)

λ = 9.17 × 10^-8 m

So the longest wavelength photon is (b) λ = 1.94 × 10^-6 m

So the shortest wavelength photon is (d) λ = 9.17 × 10^-8 m