Question

Consider the three electronic transitions in a hydrogen atom shown here, labeled A, B, and C. 

(a) Three electromagnetic waves, all drawn on the same scale, are also shown. Each corresponds to one of the transitions. Which electromagnetic wave (i), (ii), or (iii), is associated with electronic transition C?

(b) Calculate the energy of the photon emitted for each transition.

(c) Calculate the wavelength of the photon emitted for each transition. Do any of these transitions lead to the emission of visible light? If so which one(s)? {Section 6.3)

Answer 1

b) Energy or wavenumber (ν) = R_H (1/n₁² - 1/n₂²)

A. n1 = principal quantum number of lower energy level = 1

n2 = principal quantum number of higher energy level = 2

R_H = 1.09737×10⁷ m⁻¹

ν = 1.09737×10⁷ m⁻¹( 1/1 - 1/4 )

= 0.82303 * 10⁷ m^-1

Wavelength(λ) = 1 / E = 121.5 nm

corresponds to lymann series

B. n1 = principal quantum number of lower energy level = 2

n2 = principal quantum number of higher energy level = 3

R_H = 1.09737×10⁷ m⁻¹

ν = 1.09737×10⁷ m⁻¹( 1/4 - 1/9 )

= 0.1525 * 10⁷ m^-1

Wavelength(λ) = 1 / E = 655.7 nm

corresponds to Balmer series

C.n1 = principal quantum number of lower energy level = 3

n2 = principal quantum number of higher energy level =4

R_H = 1.09737×10⁷ m⁻¹

ν = 1.09737×10⁷ m⁻¹( 1/9 - 1/16 )

= 0.05323 * 10⁷ m^-1

Wavelength(λ) = 1 / E = 1878.64 nm

corresponds to Paschen series

Among the three transitions, transition shown in B is actually falling under the visible region. As the wavelength observed falls under the visible region of 400-800 nm