102 nm wavelength of light is emitted when the electron in a hydrogen atom relaxes from n= 3 to n= 1
∆E = - Rh × ( 1/nf² - 1/ni² )
∆E = difference in energy between final and initial energy level (J )
R = Rydberg's constant
nf = final energy level
ni = initial energy level
nf = 3, ni = 1, Rh = 2.18 × 10-¹⁸
∆E = -2.18 × 10-¹⁸ ( 1/3² - 1/1² )
= 2.18 × 0.88 × 10-¹⁸ J
∆E = 1.93 × 10-¹⁸ J
∆E = hf = hc / λ
λ = (h × c) / ∆E
= ( 6.625 × 10-³⁴ × 3 × 10⁸) / 1.93 × 10-¹⁸
= 19.878 × 10-²⁶ / 1.93 × 10-¹⁸
= 10.299× 10-⁸
= 102.99×10-⁹
= 102 nm
Learn more about Rydberg's constant at https://brainly.com/question/23737904
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