# Bohr model and energy

#### mss90

Hi guys, my first post on this forum.
I was wondering if anyone could help me crack this nut:

Using the Bohr model of the atom:
(i) What would you expect the lowest energy transition from the n=2 to n=1
state to be for single electron ions of the following elements.
(ii) What would be the corresponding Bohr radii for the n=1 states in such
systems?
a. hydrogen (Z=1)

Cheers

#### topsquark

Forum Staff
Hi guys, my first post on this forum.
I was wondering if anyone could help me crack this nut:

Using the Bohr model of the atom:
(i) What would you expect the lowest energy transition from the n=2 to n=1
state to be for single electron ions of the following elements.
(ii) What would be the corresponding Bohr radii for the n=1 states in such
systems?
a. hydrogen (Z=1)

Cheers
For both questions we need the formula for the radius for a one electron ion:
a_n = (n^2/Z) * (constant)

So for n = 1, the larger the Z the lower the energy.

-Dan

#### mss90

alright this is what i did;

En = -13.6eV*Z2/n2
n=2 -> n=1 for hydrogen (Z=1)
E2= -13.6eV*12/22 =-3.4 eV
E1= -13.6eV*12/12 = -13.6 eV
deltaE = x1 – x2 = -3.4 + 13.5 = 10.2 eV
So 10.2 eV is the lowest energy transition from n2 to n1 right?

Does the constant change with elements?

#### topsquark

Forum Staff
alright this is what i did;

En = -13.6eV*Z2/n2
n=2 -> n=1 for hydrogen (Z=1)
E2= -13.6eV*12/22 =-3.4 eV
E1= -13.6eV*12/12 = -13.6 eV
deltaE = x1 – x2 = -3.4 + 13.5 = 10.2 eV
So 10.2 eV is the lowest energy transition from n2 to n1 right?

Does the constant change with elements?
First you need to use exponential notation. 12 is not the same as 1! In "text" code we use ^ for powers: 2^2 and 1^2 respectively.

Yes, this is the lowest energy. The transition from n = 2 to n = 2 would be -13.6*Z^2*(1/2^2 - 1/1^2) eV. Since Z is larger than one for anything but hydrogen, the levels for hydrogen will be the smallest.

Yes, Z changes. Z is the atomic number of the element.

-Dan

#### Pmb

PHF Hall of Fame
First you need to use exponential notation. 12 is not the same as 1! In "text" code we use ^ for powers: 2^2 and 1^2 respectively.

Yes, this is the lowest energy. The transition from n = 2 to n = 2 would be -13.6*Z^2*(1/2^2 - 1/1^2) eV. Since Z is larger than one for anything but hydrogen, the levels for hydrogen will be the smallest.

Yes, Z changes. Z is the atomic number of the element.

-Dan
Hi Dan,

I know that it's been a while since I've posted here but it seems like you're no longer requiring people to post what they've done before giving them help. Is that the case? And are you doing the entire problem for them now?

#### topsquark

Forum Staff
Hi Dan,

I know that it's been a while since I've posted here but it seems like you're no longer requiring people to post what they've done before giving them help. Is that the case? And are you doing the entire problem for them now?
(shrugs) The OP did the actual work. I simply mentioned the equation.

-Dan

PHF Hall of Fame
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#### topsquark

Forum Staff
I don't understand what "shrugs" means. Please explain.
A "shrug" is raising your shoulders indicating a lack of worry.

-Dan

#### Pmb

PHF Hall of Fame
A "shrug" is raising your shoulders indicating a lack of worry.

-Dan
I see. The reason I ask is because some people use it to indicate that someone is being stupid. Since that doesn't sound like a way that you'd treat me I had to ask. Thanks my friend. #### THERMO Spoken Here

What Time? Time to Improve PHF Input Interface.

(shrug) Hi Everybody,

I enjoy looking through the entries at PHF. Much meaningful activity happens here. However there is unnecessary, useless stuff at PHF.

I must agree completely with Pmb. I also don't know what "shrugs" means. I don't know what "cool" means, nor "Nod," nor
"Headbang," nor "Itwasntme," nor "Nerd" nor any of the other 11 bullshit smilies to the right of the too-narrow text box for POST writing.
The "text-area" input box has 15 stupid options to the right and 14 more options below. Me and "Pmb" don't know what these mean.

Can some intelligent person get these juvenile faces off the formatted INPUT interface and to hell out of PHF?

I asked this before (Someone in the office at PHF likes these baby faces). AT LEAST, I ask, could that someone start a THREAD so we
can all learn what "shrug" and all the other crap faces mean?