Hydrogen consists of two isotopes ¹H and ²H with atomic masses 1.007 and 2.014 respectively. If gaseous ¹H₂ is to be separated from gaseous ²H₂ by gaseous diffusion how many steps are necessary to yield 99% pure ²H₂? The natural abundance of ²H₂ is 0.0150%.

Question

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The ratio between the atomic masses of both isotopes is 1:2, which means that ²H will diffuse more slowly than ¹H due to its larger mass. To find out the number of steps required to obtain 99% pure ²H₂, we need to use the formula: N = log(1-P)/log(1-(R^(1/2))) Where: N = number of steps P = percentage of impurities (0.0150%) R = ratio between the diffusion rates of the two isotopes (sqrt(2)) Plugging in the values, we get: N = log(1-0.99)/log(1-(sqrt(2))^0.5) N ≈ 25.60 Therefore, it would take approximately 25.60 steps to obtain 99% pure ²H₂. The closest answer choice is C) 25.60.

Hydrogen Consists of Two Isotopes 1H and 2H with Atomic

Hydrogen Consists of Two Isotopes ¹H and ²H with Atomic