Question

a molecule of o2 and o3 travel with same velocity.what is the rate of their wave length.

Answer 1

O2 is with higher wave length than O3.

Answer 2

Answer: The ratio of the wavelengths of $O_2:O_3$ is 3 : 2

Explanation: To relate the wavelength with velocity, we use De-Broglie's Equation, which is:

$\lambda=\frac{h}{p}$

and

p = mv

Putting the value of 'p' in above equation, it becomes:

$\lambda=\frac{h}{mv}$

where, h = Planck's constant

m = mass of the particle

v = velocity of the particle

$\lambda$ = Wavelength of the particle

We are given two molecules, the mass of both the molecules is:

Mass of $O_2=16\times 2=32amu$

Mass of $O_3=16\times 3=48amu$

As, the velocity of both the molecules is same.

The wavelength of $O_2$ is: $\lambda_1=\frac{h}{32v}$

The wavelength of $O_3$ is: $\lambda_1=\frac{h}{48v}$

Taking ratios of both the molecules:

$\frac{\lambda_1}{\lambda_2}=\left(\frac{\frac{h}{32v}}{\frac{h}{48v}}\right)\\\\\frac{\lambda_1}{\lambda_2}=\frac{48}{32}$

$\lambda_1:\lambda_2=3:2$

Hence, the ratio of the wavelengths of $O_2:O_3$ is 3 : 2