Physics · Kinetic theory of gases: assumptions, the concept of pressure, kinetic interpretation of temperature
The average of molecules in a gas at temperature is Find the temperature at whic
The average \( K E \) of molecules in a gas at temperature \( T \) is \( \frac{3}{2} k T . \) Find the temperature at which the average KE of molecules equal to binding energy of its atoms.
- A. \( 1.05 \times 10^{5} K \)
- B. \( 1.05 \times 10^{4} K \)
- C. \( 1.05 \times 10^{3} K \)
- D. none of these
Step-by-step solution
The average kinetic energy is (3/2)kT. Setting this equal to the binding energy of a hydrogen atom (13.6 eV) and solving for T gives T = (2/3)(13.6 eV)/k. Converting eV to joules (1 eV = 1.6×10^(-19) J) and using k = 1.38×10^(-23) J/K yields T ≈ 1.05×10^5 K.
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