An atom of carbon has a radius of 67.0 pm and the average orbital speed of the electrons in it is about 1.3 x 10⁶ m/s.
calculate the least possible uncertainty in a measurement of the speed of an electron in an atom of carbon. write your answer as a percentage of the average speed, and round it to significant digits.

Answer :

The least possible uncertainty in an electron's velocity is,

The percentage of the average speed is, 33 %

Explanation :

According to the Heisenberg's uncertainty principle,

...........(1)

where,

= uncertainty in position

= uncertainty in momentum

h = Planck's constant

And as we know that the momentum is the product of mass and velocity of an object.

or,

     .......(2)

Equating 1 and 2, we get:

Given:

m = mass of electron =

h = Planck's constant =

radius of atom =    

= diameter of atom =

Now put all the given values in the above formula, we get:

The minimum uncertainty in an electron's velocity is,

Now we have to calculate the percentage of the average speed.

Percentage of average speed =

Uncertainty in speed =

Average speed =

Percentage of average speed =

Percentage of average speed = 33.2 % ≈ 33 %

Thus, the percentage of the average speed is, 33 %

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i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles  

b) 0.4 miles  

c) 1 mile  

d) 3.15 miles