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PointAn electronis measured to have momentum 81.8andto be atalocation 92nmn . Whatis the minimum uncertainty of thee lectron" position (in nm)?Type your answer...

Question

PointAn electronis measured to have momentum 81.8andto be atalocation 92nmn . Whatis the minimum uncertainty of thee lectron" position (in nm)?Type your answer_

point An electronis measured to have momentum 81.8 andto be atalocation 92nmn . Whatis the minimum uncertainty of thee lectron" position (in nm)? Type your answer_



Answers

The uncertainty in a proton's position is 0.010 $\mathrm{nm}$ . (a) What
is the minimum uncertainty $\Delta p$ in its momentum? (b) What is
the kinetic energy of a proton whose momentum is equal to this
uncertainty $(\Delta p=p) ?$

Uncertainty in position. Delta X it's equal to 0.10 nanometer, 0.1090 meter is equal to 0.10 multiplied by 10 to the power minus nine meter party. We need to find out uncertainty in momentum, according to Heisenberg. Uncertainty principle, uncertainty, momentum Times answer. A certainty in position is equal to each divided by two by and Delta P uncertain Teen momentum is equal to each divided by two by times until tax Oh, let's substitute, uh, values. It is 6.63 Multiply the 10 to the power minus 34 divided by do multiply by 3.14 multiplied by Delta X, which is considered a 0.10 multiplied by 10 to the dollar minus nine. And this, uh, this gives us, uh, 105 105 point 57 Multiply. We tend to the power minus 25 and, uh, this can be fun. The returnees one point 05 multiplied by 10 to the power minus 23 kilogram mater per second. So uncertainty and momentum is equal to 1.5 Multiply pretend to the power minus, uh, 23 kilogram meters per second. No, let's sold part B. Well, we know that kinetic energy is equal to P square, divided by two times Mars bees Momentum and M is the mass of electron. In this case, uncertainty momentum equals B, then for B is equal to 1.5 multiplied by 10 to the power minus 23 kilogram meter per second. But kinetic energy equals up. B is 1.5 Multiply by 10 to the power minus 23. Ah, whole square divided by this is five, um, divided by ah, we have two times months of electron and most of electron. He's a 9.1 multiply by 10 to the power minus 30 bun and therefore our kinetic energy is equal to, um, 6.6 points. It'll multiply by 10 to the power minus 17 jewels. Let's gun work into electron waltz. So we have six points, you know, multiply by 10 to the power minus 17. Divided by 1.6, multiply returned to the power minus 19 jewels, which is equal to one electron. Walt. Therefore six ones. It'll multiply. Returned to the bar minus 17 jewels is equal to ah 0.3750 point 375 Multiply by 10 to the power free electron votes and this can be written knees. Ah, kinetic energy is equal to 0.375 kilo electron walked.

So we want to know the position uncertainty off a certain electron woods philosophy as a certain uncertainty that is given to us. So the velocity uncertainty is three points for these minus 3.48 thanks them to the fire meters per second. So this gives us have a lot of uncertainty off one times 10 to the four meters per second. And we know that the Heisenberg uncertainty principle tells us that build a x times delta p the direction should be age over to right. So we know that Delta P X is, um the ex red so we can rent this in this way, the eggs is age over Jewell, and in this case, the mass is off the electric. So oh, with your literal mass delta be next and this is simply so. I'll use that six months 63. Thanks. Then do the minus 34 Jules time. Second is the plan constant. This is two times nine points. 11 times 10 to the minus. Sorry, 10 to the minus 31 times, then to the fore meters per second. This gives around 3.6 times. Stand to the man is eight meters, which is 36 nanometers. So the answer is just a few atomic. The amateurs

As here I can write. The value of the legs is equal to 0.15 nm just changing the unit into meat, multiplying it by 10 to the power minus 9 m by one nm. So on simplifying it, I get the value edge 0.15 into 10. 30 part minus 9 m now solving party. So for party, we have the L P. Is greater than is equal to edge by 25 day legs. So I will just put the value here so I can write. It is greater than is equal to 6.63 into 10 to the minus 30. For Jules, I can buy to buy multiplication 0.15 into 10 to the power minus 9 m So they'll be is greater than is equal to seven into 10 to the power minus 25 kg meted per second. As our final answer for party now going forward and calculating the kinetic energy of the pro tune. So I will use the formula K is equal to Dell P Square by two. And so just putting the value here I can write K is equal to 7.4 into 10 to depart, minus 25. Holy Squared by to multiplication 1.673 into 10 to depart minus 27 which is equal to 1.5 into 10 to the power minus 22 jewel approx.

From high ginsburg unsent entity principle, I can write the value of Dell X. Multiplication. DLP is greater than is equal to urge by two pi. It can be further return it DLP is greater than is equal to edge by two pi multiplication, one by day legs, simplifying it further. Just putting the value in this expression I can like it is greater than equal to 6.63 multiplication than 10 to the power minus 34 jules, second by two pi multiplication, one by 10.2 m, which is equal to 5.279 multiplication and 10 to the power minus 34 kg meter pulse again. So this is the minimum uncertain entity in the momentum of the ball. So this is our final answer.


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