A beam of electrons with of wavelength of 7.5 x 10-6 m is incident on a pair of narrow rectangular slits separated by 0.75 mm. T
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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 %