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Obtain an order-of-magnitude value for the temperature at which helium might begin to exhibit quantum/ superfluid behaviour. See equation (9.43). (Helium's specific gravity is about 0.12.)

Short Answer

Expert verified

Temperature for helium atom is0.0094K.

Step by step solution

01

Formula used 

NVn3(mkBT)32<<1

Where,

NNumber of particles

VVolume

Planck's reduced constant

mMass of the object

kBBoltzmann' constant

TTemperature.

02

Calculate temperature for helium

Converting mass of helium from u to kg unit

mA=4u=(4u)1.661027kg1u=6.641027kg

NV3(mkBT)32<<1NV3<<(mkBT)32NV322<<mkBTT>>2mkRNV23

The N/V can be rewritten as the mass per unit volume over the mass per atom (or just the mass of an atom), or the bulk density Dover the atomic mass m.

T>>2mkBNV23>>2mkRNV23

The specific gravity of helium is 0.12, so the density of the helium is 0.12 times that of density of the air, which has an approximate density of 1.2kg/m3. Therefore, its density of helium is

D=0.12(Dair)

Substitute 1.2kg/m3for density of the air Dair.

D=(0.12)(1.2kg/m3)=0.144kg/m3

Substitute 0.144kg/m3 for D,1.381023J/K for kB,1.0551034Js and mAfor 6.64 1027kg

2mkBDm23=(1.0551034Js)2(6.641027kg)(1.381023J/K)(0.144kg/m3)(6.641027kg)23=0.0094K,

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