## h/4pi

$\Delta p \Delta x\geq \frac{h}{4\pi }$

Will Pham 1J
Posts: 57
Joined: Wed Sep 30, 2020 10:00 pm

### h/4pi

If we know the value of h/Planck's constant as 6.626 x 10^-34 J*s and the value of pi rounded as 3.14, why is h/4pi always written if it is a constant?

Ashley Ko 3I
Posts: 63
Joined: Wed Sep 30, 2020 9:54 pm

### Re: h/4pi

Hi! So, I believe it is written as h/(4pi) because it is more accurate to do so. If you divide h by 4pi, you get a really long, complicated number and would have to round to write it as a constant. As a result, calculations would be less accurate. Hope this helps!

Jayasree Peri 2J
Posts: 67
Joined: Wed Sep 30, 2020 10:03 pm

### Re: h/4pi

I agree with Ashley! When you plug pi into a calculator, it uses more than just 3.14 (it's easier to type in pi as well).

JoshMoore2B
Posts: 55
Joined: Wed Sep 30, 2020 9:51 pm

### Re: h/4pi

Will Pham 2I wrote:If we know the value of h/Planck's constant as 6.626 x 10^-34 J*s and the value of pi rounded as 3.14, why is h/4pi always written if it is a constant?

I believe another reason why h/4pi is always written out as opposed to some other, new constant (let's call it Q), is because h itself is a constant that is used very frequently elsewhere in the science world. Therefore, it is easier to recognize and plug in its value into the equation as opposed to having to recognize Q and plug that value in.

If every time we manipulated a constant for the sake of an equation we made a new constant to represent that manipulation, then our list of constants would be very long!

Joel Meza 3I
Posts: 56
Joined: Wed Sep 30, 2020 9:56 pm

### Re: h/4pi

We use h/4pi because writing out the actual value of this constant wouldn't be convenient. It is much easier to write this out as h/4pi and then plug in the values into the calculator when it comes time to do so in the question.

Nick P 3D
Posts: 56
Joined: Wed Sep 30, 2020 9:42 pm

### Re: h/4pi

It likely is written this way because it already includes two constants within itself. Creating a third constant would likely just cause unnecessary memorization when two other very common constants, Planck's and pi, can simply be used to calculate it each time. In addition, pi and Planck's constant are both not very nice numbers, meaning h bar would need to be either rounded or truncated which would just reduce its accuracy.

Jonathan Banh 1G
Posts: 60
Joined: Wed Sep 30, 2020 9:33 pm

### Re: h/4pi

I believe $\frac{h}{4\pi}$ is written out for both convenience and accuracy. Since both Planck's constant and π are constants, there is not really a need to create another constant from them, instead just using our known values of constants instead. Also, like others said, it is much easier to typing these out in your calculator this way. In terms of accuracy, π is not just simply "3.14", although it may seem like it, and $\frac{h}{4\pi}$ will not provide a easy-to-use number, so it is much better to write it out to ensure accuracy in your final calculations.

Griffin G
Posts: 54
Joined: Wed Sep 30, 2020 9:50 pm

### Re: h/4pi

This is, more than anything, a convention. We could set some random letter to equal h/4pi, but regardless you'd have to plug h/4pi into your calculator each time, because pi is an irrational number. You COULD simply memorize a simplified version of h/4pi, but then your answers would lose accuracy.