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

answer : third trial had the contaminated sample and the correct value for dhrxn should be 1000 kj/mol

explanation :

let us write down the given equations

equation 1 :

equation 2 :

equation 3 :

let us use hess's law to find out which 2 equations can be added to get the third equation.

let us reverse equation 2 and multiply it by 2. the new equation that we get is,

equation 4 :

let us add equation 1 & 4

the above equation is similar to equation 3 but has different value for dhrxn.

therefore third trial had the contaminated sample and the correct value for dhrxn should be 1000 kj/mol