An electron has an uncertainty in its position of 552 pm. What is the uncertainty in its velocity?

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Hey everyone. And welcome back, an electron has an uncertainty in its position of 552 Peters, what is the uncertainty in its velocity were given for answer choices. A three multiplied by 10 to the eighth B two multiplied by 10 to the third. C 1.0 multiplied by 10 to the fifth and D 3.0 multiplied by 10 to the seventh. We are going to solve this problem using the Heisenberg uncertainty principle which states that delta X multiplied by delta P is greater than or equal to H divided by four pi. Now let's understand the terms. So delta X is the uncertainty in position. Delta P is the uncertainty in momentum H is the Plank's constant. And let's remember that delta P, the uncertainty and momentum can be expressed as the product between mass and the uncertainty and velocity. So this allows us to obtain a different formula or a slightly rearranged formula such that M delta X delta V should be greater than or equal to H divided by four pi. And because we are solving for the uncertainty and velocity, we can rearrange the formula for delta V which is greater than or equal to H divided by four five M delta X. And now we can just substitute the guns, right. So the uncertainty and velocity would be our planks constant. So we're going to use 6.626 multiplied by 10 of the power of negative 34th, Juul multiplied by second. And now we need to divide that by four pi multiplied by the mass. Now, what is the mass of an electron? Well, essentially we have to recall that we need to use it in kilograms. That'll be 9.109 multiplied by 10 to the power of negative 31st kilograms. And that we also need to include the uncertainty and position. We are given 552 Peters, but we need to use meters. So we're going to include a conversion factor pledged at 1 m is equivalent to sense the power of 12 Peters. And now if we solve the given inequality, we will get the uncertainty of 1.05 multiplied by turn to the power of fifth meters per second. From here, we can conclude that the correct answer to this problem is C 1.05 multiplied by sensitive first meters per second. Thank you for watching.

An electron has an uncertainty in its position of 552 pm. What is the uncertainty in its velocity?

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Key Concepts

Heisenberg Uncertainty Principle

Quantum Mechanics

Uncertainty in Measurements