A small dust particle of mass is being observed under a magnifying lens. Its position is determined to within (

Hello!

A. The main physical law to use here is the uncertainty principle with respect to momentum and position. The formula is

ħ/2,

where is an uncertainty in a momentum, is an uncertainty in a position of the same particle, and ħ is the reduced Planck's constant,   It is obvious that where is a mass of a particle and

Hello!

A. The main physical law to use here is the uncertainty principle with respect to momentum and position. The formula is

ħ/2,

where is an uncertainty in a momentum, is an uncertainty in a position of the same particle, and ħ is the reduced Planck's constant,   It is obvious that where is a mass of a particle and is an uncertainty in its speed.

Therefore the minimum uncertainty in a velocity is  

All values are given, but we have to make m from mm and kg from g. The numerical answer is

Thus I agree with your answer. I don't even have an idea where 4.6 may come from.

B. A time is a distance divided by a speed, the only problem is to use correct units. A time in seconds is   To get this time in years we have to divide it by the given number of seconds in a year, i.e.

If we would use the speed that stated as the "correct answer" for A, the answer would be that you want as "correct" for B.