JEE Main 2023 · 29 January · evening · Single correct · +4 / −1

At 300 K, the rms speed of oxygen molecules is √((α + 5)/α) times to that of its average speed in the gas. Then, the value of α will be
(used π = 22/7)

  1. (a) 27
  2. (b) 28
  3. (c) 24
  4. (d) 32
Answer and solution

Answer (b) 28

Solution

Physics sir · 4 steps

The ratio of rms to average speed is a pure number. Temperature and the gas both cancel out.

  1. Write both speeds. For any ideal gas, vᵣₘₛ = √(3RT/M) and v_(avg) = √(8RT/(π M)). Divide one by the other and R, T and M all cancel.

    vᵣₘₛ/v_(avg) = √(3π/8)

  2. Use the given pi. With π = 22/7, 3π/8 = (3 × 22)/(7 × 8) = 66/56 = 33/28.
  3. Match the form. Set (α + 5)/α = 33/28. This gives 1 + 5/α = 1 + 5/28, so α = 28.
  4. So. α = 28, which is option (b). The 300 K and the choice of oxygen play no part in the answer.

The idea to keep. The ratio vᵣₘₛ : v_(avg) : vₘₚ = √3 : √(8/π) : √2 is the same for every gas at every temperature. Any ratio question reduces to these constants.

Answer from the NTA final answer key. Solution by PrepWiser.

Study Kinetic Theory of Gases

Asked about 130 times in JEE Main since 2020. This question is from 2023.