Question

The average speed of a diatomic chlorine molecule is 25°C, and its velocity is 323.9 m/s. What's the average wavelength of a chlorine molecule at this temperature?

a. 1.22 nm
b. 2.45 nm
c. 0.97 nm
d. 3.68 nm

Answer 1

To find the average wavelength of a chlorine molecule, apply the de Broglie wavelength formula, convert the mass of Cl2 from atomic units to kg, and then calculate the wavelength using the given velocity.

Step-by-step explanation:

To calculate the average wavelength of a chlorine molecule at a given temperature, we use the de Broglie wavelength formula λ = h / (mv), where h is the Planck constant (6.626 x 10-34 Js), m is the mass of a particle, and v is its velocity. First, calculate the mass of a chlorine molecule (Cl2) using the average relative atomic mass from the periodic table (35.5 u for Cl) and multiplying it by two, since it is diatomic, and then converting to kilograms by multiplying by 1.66 x 10-27 kg/u. Afterwards, use the given velocity to find the average wavelength.

The detailed calculation steps are as follows:

1. Calculate the mass of Cl2: (2 x 35.5 u) x (1.66 x 10-27 kg/u) = m
2. Substitute the mass (m) and given velocity (v = 323.9 m/s) into the de Broglie equation to find the wavelength (λ).

This concept is applied to different molecules under various conditions to determine their behavior in a gas.