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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Chemistry
Chapter
States of Matter

NTA Abhyas 2020 · Chemistry · States of Matter

The root mean square speed of N _ 2 molecules in sample at...

The root mean square speed of N2{N}_{2} molecules in sample at temperature T is 'x'. If the temperature is doubled, then nitrogen molecules dissociate into atoms, the root mean square speed of nitrogen atoms becomes n times of 'x' find the value of n here?

Correct answer

2

Step-by-step solution

vrms=3RTm{v}_{rms} = \sqrt{\dfrac{3RT}{m}}
x=3RT28x = \sqrt{\dfrac{3RT}{28}} …(i)
vrms=3R×2T14{v}_{rms} = \sqrt{\dfrac{3R \times 2T}{14}} …(ii)
Dividing equation (i) by equation (ii)
xvrms=14\dfrac{x}{{v}_{rms}} = \sqrt{\dfrac{1}{4}}
So, vrms=2x{v}_{rms} = 2x
So, n = 2.
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