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The temperature at which oxygen molecules have the same root mean square speed as helium atoms have at 300 K is : (Atomic masses : He = 4 u, O = 16 u)

Options

  1. A600 K
  2. B2400 K
  3. C1200 K
  4. D300 K

Correct answer

B. 2400 K

Step-by-step solution

C rms = 3 RT M C rms He = 3 R × 3 0 0 4 & C rms O 2 = 3 R × T O 2 3 2 ∴ ( C r m s ) H e = ( C r m s ) O 2 ⇒ 3 R × 300 4 = 3R × T O 2 32 T O 2 = 3 0 0 × 3 2 4 = 2 4 0 0 K

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