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

the maxium height is 34m/s

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft