The mass of the most common silicon atom is 4.646 * 10-26 kg, and the mass of the most common oxygen atom is 2.656 * 10-26 kg. When a molecule of silicon monoxide (SiO) makes a transition between the l = 1 and l = 0 rotational levels, it emits a photon of wavelength 6.882 mm. Find the distance between the Si and O nuclei.

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The mass of the most common silicon atom is 4.646 * 10-26 kg, and the mass of the most common oxygen atom is 2.656 * 10-26 kg. When a molecule of silicon monoxide (SiO) makes a transition between the l = 1 and l = 0 rotational levels, it emits a photon of wavelength 6.882 mm. Find the distance between the Si and O nuclei.

Expert Solution
Step 1

Given data:mass of silicon,msi = 4.646 × 10-26 kg mass of oxygen,m0 = 2.656 ×10-26 kgtransition from  l =1  to l = 0andwavelength λ = 6.882 mm = 6.882 × 10-3 m

Step 2

Here,reduced mass,μ =  msi × momsi + m0μ =  4.646 × 10-26 × 2.656 × 10-26( 4.646 + 2.656) ×10-26μ = 1.69 × 10-26 kg

Step 3

formula for energy eigen value,El = h28  π2I l ( l + 1)soE1 = h28  π2I1 ( 1 + 1) E1 =2 h28 π2 I ...................eq(1)simillarlyE0 = h28  π2I 0 ( 0 + 1) = 0 ..............eq(2)change in energy,E= 2 h28 π2 I - 0E= 2 h28 π2 I ............................eq(3)

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