Question

Using the method of the preceding problem, estimate the fraction of nitric oxide (NO) molecules at a temperature of 250 K that have energies between 3.45×10⁻²¹ J and 3.50×10⁻²¹ J.

a) 0.01
b) 0.05
c) 0.10
d) 0.20

Answer 1

To estimate the fraction of nitric oxide molecules with energies between 3.45×10⁻²¹ J and 3.50×10⁻²¹ J at a temperature of 250 K, we can use the Maxwell-Boltzmann distribution and approximate it as a constant within the given energy range.

Step-by-step explanation:

To estimate the fraction of nitric oxide (NO) molecules at a temperature of 250 K that have energies between 3.45×10⁻²¹ J and 3.50×10⁻²¹ J, we can use the Maxwell-Boltzmann distribution. The fraction of molecules with energies in a certain range can be calculated by integrating the distribution function over that range. Since the energy range is small, we can approximate the distribution function as a constant within that range.

The fraction of molecules with energies between E₁ and E₂ is given by:

f(E₁,E₂) = ∫ f(E) dE ≈ f(E₁) ΔE

Substituting the given values, we have:

f(E₁,E₂) ≈ f(E₁) ΔE = f(E) ΔE = ΔE e^(-E/kT)

where ΔE is the difference in energies, E is the average energy, k is Boltzmann's constant, and T is the temperature. Plug in the values and simplify the expression to calculate the fraction of nitric oxide molecules with energies between 3.45×10⁻²¹ J and 3.50×10⁻²¹ J.