What is the de-Broglie wavelength of nitrogen molecule in air at 300K ? Assume that the molecule is moving with the root mean square speed of molecules at this temperature. (Atomic mass of nitrogen `=14.0076U`) Plank's constant=`6.63xx10^(-34)Js` , Boltzmann constant `=1.38xx10^(-23)JK^(-1)`

Explanation

To find the de-Broglie wavelength of a nitrogen molecule in air at 300K, we will follow these steps:

### Step 1: Determine the mass of a nitrogen molecule (N2)
The atomic mass of nitrogen (N) is given as 14.0076 u. Since a nitrogen molecule is diatomic (N2), we need to multiply this value by 2.

\[ \text{Mass of } N_2 = 2 \times 14.0076 \, \text{u} = 28.0152 \, \text{u} \]
...