Thermal de Broglie wavelength is the de Broglie wavelength of the gas particles in an ideal gas at temperature $T$ with average kinetic energy given by the equipartition theorem and usual relation between kinetic energy and momentum. Consider an ideal monoatomic gas $A$ of $N_a$ atoms, each of mass $m_a$ and another ideal monoatomic gas $B$ of $N_b$ atoms, each of mass $m_b=4 m_a$. Both gases are uniformly distributed in boxes of volume $V$ at temperature $T$. Select the correct statement(s).

• A

  If a photon has wavelength equal to thermal de Broglie wavelength of atoms of gas $A$ then the ratio of photon momentum and average momentum of atoms in gas $A$ i.e $p_{\text {photon }} / p_A$ is $2 / 3$.
• B

  If total mass of gas $A$ is same as total mass of gas $B$ then their pressures are related as $P_B=4 P_A$.
• Correct answer
  C

  Thermal de Broglie wavelengths of gases $A$ and $B$ are in ratio $\lambda_A / \lambda_B=2$.
• Correct answer
  D

  If volume and temperature are such that, for both gases A and B , the average inter-particle spacing in each direction is equal to thermal de Broglie wavelength of respective atoms $\lambda_A$ and $\lambda_B$ then $N_b=8 N_a$.

Hence, the correct answer is options: 'C', 'D'.