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The r.m.s. velocity of hydrogen is sqrt(...

The r.m.s. velocity of hydrogen is `sqrt( 7)` times the r.m.s. velocity of nitrogen. If T is the temperature of the gas `:`

A

`T_(N_(2)) = T_(H_(2))`

B

`T_(H_(2)) = sqrt( 7) T_(N_(2))`

C

`T_(N_(2)) = 2T_(H_(2))`

D

`T_(N_(2)) = sqrt(7) T_(H_(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
r.m.s. velocity `= sqrt(( 3RT)/( M))`
For hydrogen r.m.s. velocity `= sqrt(( 3RT_(H_(2)))/(2))` ....(i)
For nitrogen r.m.s. velocity `= sqrt(( 3RT_(N_(2)))/(28)) ` ....(ii)
Given that (i) `= sqrt( 7)` (ii)
`:. sqrt(( 3RT_(H_(2)))/( 2)) = (sqrt( 7)) sqrt((3RT_(N_(2)))/(28))`
or `sqrt((T_(H_(2)))/(2)) = sqrt((T_(N_(2)))/(4))`
Squaring both sides, `( T_(H_(2)))/(2) = ( T_(N_(2)))/(4)`
or `2T_(H_(2)) = T_(N_(2))`
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