Electron energy levels in Bohr model

Smythe

At the bottom of this linked-to screen below is an equation for E = - .......... = - ............. = - 13.6 Z^2 / n^2 eV

https://en.wikipedia.org/wiki/Bohr_model#Electron_energy_levels

I'm using the following values for the formula

Z=1
n=1
K sub e = 8.987 x 10^9 (Coulombs constant)
e = 2.71828
m sub e = 9.11 x 10^-31 (mass of electron)
h-bar = 1.05 x 10^-34

But when I plug these values in I get (4.017x10^-9) / (2.205 x 10^-68) = - 1.82 x 10^59

and not -13.6 eV

What am I doing wrong? Are any of my values above incorrect?

Turtwig

Smythe wrote: »

At the bottom of this linked-to screen below is an equation for E = - .......... = - ............. = - 13.6 Z^2 / n^2 eV

https://en.wikipedia.org/wiki/Bohr_model#Electron_energy_levels

I'm using the following values for the formula

Z=1
n=1
K sub e = 8.987 x 10^9 (Coulombs constant)
e = 2.71828
m sub e = 9.11 x 10^-31 (mass of electron)
h-bar = 1.05 x 10^-34

But when I plug these values in I get (4.017x10^-9) / (2.205 x 10^-68) = - 1.82 x 10^59

and not -13.6 eV

What am I doing wrong? Are any of my values above incorrect?

e isn't the exponential function. It's the charge on the electron. 1.6x10^-19 C

All your other values appear correct and should yield the correct term.

Smythe

Cheers Jernal!

Smythe

I'm trying to write a simple Excel program to allow use of that formula.

I've included my program and the formula in the Excel attachment. Would anyone know why I'm getting the VALUE! message in the A5 box?

Smythe

Of course the solution to this problem is to places = signs before the values, which I had forgotten to do...!

Smythe

I've attached the updated Excel file again.

The cell A5 displays the value in eV, currently set for n=1.

If I want to obtain the different values of Energy but for each of the values of n between 1 and 10 inclusive, how would I do this?

dlouth15

Smythe wrote: »

I've attached the updated Excel file again.

The cell A5 displays the value in eV, currently set for n=1.

If I want to obtain the different values of Energy but for each of the values of n between 1 and 10 inclusive, how would I do this?

I've modified the formula to use named cells. This makes it clearer. The range of numbers from 1 to 10 is given the name n.

Smythe

Thanks very much for that dlouth15!

I wanted to take a while there to check over it to fully understand what you had done.

I see now what you've done; I'll remember that method for future use, I'm sure it'll come in very handy.

Much appreciated!

Smythe

Just one other thing, if I delete the Energy values in cells J4 to J12 I can easily re-instate them by clicking on the J3 value and dragging downwards to fill these values in again.

If I want to go beyond n=10 it gives a VALUE! message. Would you know why this is and how I can extend beyond n=10?

dlouth15

Smythe wrote: »

Just one other thing, if I delete the Energy values in cells J4 to J12 I can easily re-instate them by clicking on the J3 value and dragging downwards to fill these values in again.

That might work but I would copy and paste the formula downward rather than dragging. Try it and see.

If I want to go beyond n=10 it gives a VALUE! message. Would you know why this is and how I can extend beyond n=10?

I have a range of cellls labeled "n". If you add numbers beyond 10 you need to extend the range down to include those numbers. A bit of extra work but I think the formula is clearer with named ranges rather than cell references.

Smythe

dlouth15 wrote: »

I have a range of cellls labeled "n".

You mean the 'I' column?

I can extend this 'I' column down further, say to 30.

However if I try to do the same with the 'J' column, that's when I'm getting the VALUE! message.

dlouth15 wrote: »

If you add numbers beyond 10 you need to extend the range down to include those numbers.

How would one go about extending the range?

dlouth15

Smythe wrote: »

You mean the 'I' column?

I can extend this 'I' column down further, say to 30.

However if I try to do the same with the 'J' column, that's when I'm getting the VALUE! message.

How would one go about extending the range?

I think the problem is that "n" only refers to the first 10 numbers. I don't use Excel but you could look up how to name a labelled column of numbers.

In the attached spreadsheet, I've named the entire column I as "n" so you don't need to keep extending the named range. I've also extended the numbers to 100 and copied the formula down.

Smythe

Thanks dlouth15.

dlouth15 wrote: »

I don't use Excel but you could look up how to name a labelled column of numbers.

I'll do that.

dlouth15 wrote: »

In the attached spreadsheet, I've named the entire column I as "n" so you don't need to keep extending the named range. I've also extended the numbers to 100 and copied the formula down.

I've tried dragging on the 'J' column in your last attachment and it creates also creates additional Energy values beyond n=100 without the VALUE! message.

dlouth15 wrote: »

I think the problem is that "n" only refers to the first 10 numbers.

If it's easy to explain, why was it not possible in the previous Excel sheet to drag and create new values for Energy, as can be done now? Or maybe it's just something I need more practice at...

dlouth15

Smythe wrote: »

I've tried dragging on the 'J' column in your last attachment and it creates also creates additional Energy values beyond n=100 without the VALUE! message.

That's because I named the entire "I" column "n" so there's no need to extend the range when numbers are added.

If it's easy to explain, why was it not possible in the previous Excel sheet to drag and create new values for Energy, as can be done now? Or maybe it's just something I need more practice at...

In the previous Excel sheet, only the numbers 1 to 10 were named n. In the second, every cell in the I column was named n. I could have simply extended the numbers to 100 and then extended n to refer to those numbers but instead I named the whole column n. This gives a bit of extra flexibility.

By the way, if you wanted to you could avoid using named ranges and just use cell references. You need to use absolute references with the physical constants so they don't change when you copy the formula down. However you would use a relative reference for the quantum number n as you want this to change for each instance of the formula.

Smythe

Okay, cheers for that. I see what you mean now. Again, many thanks.