An effective treatment for some cancerous tumors involves irradiation with "fast" neutrons. The neutrons from one treatment source have an average velocity of 3.5×107 m/s. If the velocities of individual neutrons are known to within 2.0% of this value, what is the uncertainty in the position of one of them?

4.54 * 10^-14 m

Explanation:

From Heisenberg's uncertainty principle, we can write;

Δp.Δx ≥ h/4π

Given that;

Δp =Δmv

So;

Δmv.Δx ≥h/4π

Δmv =2/100(3.5×10^7 m/s * 1.66 * 10^-27)

Δmv =1.162 * 10^-21 Kgms-1

Δx ≥6.63 * 10^-34 /4 * 3.142 * 1.162 * 10^-21

Δx ≥4.54 * 10^-14 m

in scientific notation, the value of the  speed of light in a vacuum

  will be written as 2.995 * 10^8. when this value is represented in the form of

  a * 10^b, then, a = 2.995 and b = 8.

the value of the speed of light in a vacuum given above can also be rounded up to approximately 300000000. in this case, the scientific notation will be written as 3 *10^8.