Question

The rms speed of oxygen molecule in a gas is u, If the temperature is doubled and the molecules dissociates into two atoms, the rms speed will be ______.

Options

• 4u

• u

• 2u

• u`sqrt2`

Answer 1

The rms speed of oxygen molecule in a gas is u, If the temperature is doubled and the molecules dissociates into two atoms, the rms speed will be 2u.

Explanation:

rms speed of O₂ molecule = u

i.e., u = `sqrt((3"RT")/"M")`    ...(i)

where, T = temperature and
M = molecular mass.

When temperature is doubled, then O₂ dissociates into two atoms.

Hence, the atomic mass of oxygen atom,

(M') = `"M"/2`

∴ rms velocity of oxygen atom

u' = `sqrt((3"RT'")/("M'")) = sqrt((3"R" * 2"T")/("M"/2))    .....[("T'" = 2"T"),("M'" = "M"/2)]`

`= 2sqrt((3"RT")/"M")`

= 2u    ...[from Eq. (i)]