Question

At what temperature will urms for Ne(g) be the same as urms for He at 350 K ?

Answer 1

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Answer 2

Given: The rms for Ne(g) be the same as rms for He at 350 K.

To find: We have to find the temperature of Ne.

Solution:

The rms speed of the gas is given as-

rms=$\sqrt{\dfrac{3RT}{M}}$.

Where R is the Rydberg constant.

M is the molecular mass of the gas.

For Ne, M is 20 and for He, M is 4 grams.

T is the temperature of the gas.

For He gas T=350K.

Let the temperature for Ne be x.

So, we can write-

$\sqrt{\dfrac{3R \times 350}{4}} =\sqrt{\dfrac{3Rx }{20}} \\ \frac{ \sqrt{350} }{2} = \frac{ \sqrt{x} }{ \sqrt{20} } \\ \frac{350}{4} = \frac{x}{20} \\ x = 1750$

The value of x is 1750.

Thus, the temperature of the Ne gas is 1750K.