The atomic masses of He and Ne are 4 and 20   amu , respectively. The value of the de Broglie…

The atomic masses of He and Ne are 4 and 20 amu, respectively. The value of the de Broglie wavelength of He gas at -73° C is "M" times that of the de Broglie wavelength of Ne at 727° C. M is:

Solution

DeBroglie wave length is given as
λ = h 2 m K.E = h 2 m 3 2 k b · T = h 3 k b m T
k b is Boltzmann's constant
λ He = h 3 k b 2 0 0 4 × 1.66 × 1 0 - 2 7 } T = 200 K m He = 4 × 1.66 × 1 0 - 2 7  kgs
λ Ne = h 3 k b 1 0 0 0 2 0 × 1.66 × 1 0 - 2 7 } T = 1000 K m Ne = 2 0 × 1.66 × 1 0 - 2 7  kgs
λ He λ Ne = 1 0 00 × 2 0 2 0 0 × 4 = 2 5 = 5

Asked in: JEE Advanced 2013 (Paper 1)

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