Question

A molecule of O2 and that of SO2 travels with the same velocity. what is the ratio of their wavelength?​

Answer 1

Answer: The ratio of wavelength of $O_2:SO_2$ is 2 : 1

Explanation:

We are given:

$v_{O_2}=v_{SO_2}$

De-Broglie wavelength is calculated by using the formula:

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

where,

$\lambda$ = wavelength of particle

h = Planck's constant

m = mass of particle

v = velocity of particle

We know that:

Mass of oxygen molecule = 32 g/mol

Mass of sulfur dioxide molecule = 64 g/mol

Taking ratios of their wavelengths, we get:

$\frac{\lambda_{O_2}}{\lambda_{SO_2}}=\left(\frac{\frac{h}{m_{O_2}\times v_{O_2}}}{\frac{h}{m_{SO_2}\times v_{SO_2}}}\right)\\\\\frac{\lambda_{O_2}}{\lambda_{SO_2}}=\left(\frac{\frac{h}{32\times v_{O_2}}}{\frac{h}{64\times v_{SO_2}}}\right)\\\\\frac{\lambda_{O_2}}{\lambda_{SO_2}}=\frac{64}{32}=\frac{2}{1}$

Hence, the ratio of wavelength of $O_2:SO_2$ is 2 : 1