Calculate the wave number for the infrared absorption of D35Cl when there is a transition from v=0 to v=1 (Unit: cm^-1, 4-digit accuracy). Use k=4.808 x 10^2 N/m for your calculations. Please refer to Math Reference.

wave number = 0.3348 * 10⁻⁸ cm⁻¹

Explanation:

Given data:

K = 4.808 * 10^2 N/m

Determine the wave number for the infrared absorption

considering vibrational Spectre

k' =  2n / λ ( 1 )

λ = c / v ( 2 )

v = √k / u  --- ( 3 )

where : k' = wave number, λ = wavelength, c = velocity of light, v = frequency,  k = force constant, u = reduced mass

u = 1.90415 for  D35Cl

Input equations 2 and 3 into equation 1 to get the final equation

K' = 2n/c * √k / u

   = ( 2 * 3.14 ) / 2.98 * 10^8  ] * (√ 4.808 * 10^2 / 1.90415 )

   = 33.486 * 10⁻⁸ m⁻¹  ≈ 0.3348 * 10⁻⁸ cm⁻¹