Question

Physical Chemistry: Ch 11 Quantum Mechanics: Model Systems and the Hydrogen Atom

(a)A hydrogen atom bonded to a surface is acting as a harmonic oscillator with a classical frequency of 6.000 × 10¹³ s ⁻¹ . What is the energy difference in J between quantizedenergy levels? (b) Calculate the wavelength of light that must be absorbed in order for the hydrogen atom to go from one level to another. (c) To what region of the electromagnetic spectrum does such a wavelength belong?

Answer:

(a) 3.976 × 10⁻²⁰ J (b) 5.00 µm

Answer 1

(a)A hydrogen atom bonded to a surface is acting as a harmonic oscillator with a classical frequency of 6.000 × 10¹³ s ⁻¹ . What is the energy difference in J between quantizedenergy levels?

E=hv
h = planck constant
v = frequency = 6.000 × 10¹³ s ⁻¹
h = 6.63 ×10^−34 Js


E = 6.63 ×10^−34 J s   * 6.000 × 10¹³ s ⁻¹

= 3.976 x10^-20 J

(b) Calculate the wavelength of light that must be absorbed in order for the hydrogen atom to go from one level to another

Frequency = velocity of light / wavelength

C= 3 × 10^8m/s; v = frequency = 6.000 × 10¹³ s ⁻¹

Wavelength = 3 × 10^8m/s / 6.000 × 10¹³ s ⁻¹

Wavelength = 0.5 × 10^-5 m

1.00 m = 1*10^6um

0.5 × 10^-5 m = 5.00um

c) To what region of the electromagnetic spectrum does such a wavelength belong?

The Mid-wavelength infrared region is 3–8 µm , and it is 5.00 µm thus it comes in IR region.