A molecule of roughly spherical shape has a mass of 6.10 x 10-25 kg and a diameter of 0.70 nm. The uncertainty in the measured position of the...

Hello!

This problem is similar to the previous. The uncertainty principle states that both position and velocity of a particle cannot be measured exactly. Mathematically,

`Delta p*Delta x gt= bar h/2,`

where `p` is for impulse (momentum), which is equal to `m*v,` mass by velocity, and `x` is the position. Correspondingly, `Delta p` means uncertainty of measuring momentum and `Delta x`  means uncertainty of measuring position. Obviously `Delta p = m*Delta v.`

`bar h` is the so-called reduced Planck's constant, `h/(2 pi).` Therefore the minimum uncertainty in the speed is

`Delta v = h/(4pi)*1/(m*Delta x).`

All quantities are given, so the numerical result is

`Delta v approx (6.626*10^(-34))/(4*3.14)*1/(6.10*10^(-25)*0.7*10^(-9)) =(6.626)/(4*3.14*6.10*0.7) approx0.1235 (m/s).`

I took into account that nano- means `10^(-9).`

To obtain the result you want one should "forget" to divide by `2pi,` then it would be about 0.7759 m/s, C. But I'm almost sure about the values.

The second question, about the minimum speed, requires a separate consideration.