The de Broglie wavelength of an oxygen molecule at 27^ C is x 10⁻¹² ~m . The value of x is (take Planck's constant =6.63 10⁻³⁴ ~J . s , Boltzmann constant =1.38 10⁻²³ ~J / K , mass of oxygen molecule =5.31 10⁻²⁶ ~kg )

Step-by-step solution

The de Broglie wavelength is = h mv . For an ideal gas, v_ rms = 3kT m Therefore: = h 3mkT Substituting values: = 6.63 10⁻³⁴ 3 5.31 10⁻²⁶ 1.38 10⁻²³ 300 = 6.63 10⁻³⁴ 6.62 10⁻⁴⁶ = 6.63 10⁻³⁴ 2.57 10⁻²³ = 2.58 10⁻¹¹ m = 25.8 10⁻¹² m, so x 26