Question

1.Calculate the frequency and wavenumber of O-H bond if the force constant and
reduced mass of the atom pair 770Nm' and 1.563 x 10-27 kg respectively​

Answer 1

Answer:

1.Calculate the frequency and wavenumber of O-H bond if the force constant and

reduced mass of the atom pair 770Nm' and 1.563 x 10-27 kg respectively is the ANSWER YES

Answer 2

Answer:

The frequency and wave number of the O-H bond are 1.12×10¹⁴ Hz and 3731.34 cm⁻¹ respectively.

Explanation:

Given:

Force constant (k) = 770N/m = 770 kg/s²

Reduced mass (m) = 1.563×10⁻²⁷kg

To find:

Frequency (ν) and wave number (n)

Step 1:

We know that the angular velocity is given as the square root of the force constant divided by the reduced mass of the system.

$w=\sqrt{\frac{k}{m} }$

Substituting the given values, we get

$w = \sqrt{\frac{770}{1.563*10^{-27}} }$

w = 7.01×10¹⁴ rad/s

Step 2:

Frequency is given as

ν = w/2π

ν = (7.01×10¹⁴ )/2π

ν = (7.01×10¹⁴ )/6.28

ν = 1.12×10¹⁴ Hz

Step 3:

c = λν

λ = c/ν

λ = (3×10⁸)/(1.12×10¹⁴)

λ = 2.68×10⁻⁶ m

λ = 2.68×10⁻⁴ cm

The wave number is given as the reciprocal of the wavelength. Therefore,

n = 1/λ

n = 1/2.68×10⁻⁴

n = 3731.34 cm⁻¹

Therefore, the frequency of the O-H bond is 1.12×10¹⁴ Hz and the wave number is 3731.34 cm⁻¹.

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