Question

Alveoli are the tiny sacs of air in the lungs whose average diameter is 50 pm. Consider an oxygen molecu
trapped within a sac. Calculate uncertainty in the velocity of oxygen molecule?
(A) 1.98 x 10-ms-1
(B) 19.8 ms-1 (C) 198 x 104 ms-1 (D) 19.8 x 106ms-1​

Answer 1

Answer:

Explanation:

1 pm is $10^{-12}$

Thus, 50pm = 5x$10^{-11}$

Now we have to calculate the mass of the oxygen atom

32x10^-3 kg oxygen atom = 1 atom

As, 1kg oxygen atom = 32x10^-3/6.023x10^23

Thus for 5x$10^{-11}$ diameter alveoli the amount of oxygen atom required is = {32x10^-3/6.023x10^23}x5x10^-11

             m*Δx = $2.65*10^{-36}$

Thus, by using uncertainty equation we get that.

Δx.Δu>=h/2πm

Δu>=h/(2πm*Δx)

Δu>=$\frac{6.626*10^{-34} }{4*3.14*2.65*10^{-36} }$

Δu>=1.98m/s

Answer 2

Dear students,

● Answer -

∆v = 19.88 m/s

◆ Explanation -

# Given -

∆x = 50 pm = 5×10^-11 m

m = 5.3×10^-26 kg

# Solution -

Uncertainty in the velocity of oxygen molecule is given by -

∆v = h / 4πm∆x

∆v = (6.62×10^-34) / (4×3.142 × 5.3×10^-26 × 5×10^-11)

∆v = 19.88 m/s

Therefore, uncertainty in the velocity of oxygen molecule is calculated by 19.88 m/s.

Hope I was useful.