Bohr Model of the Hydrogen atom: Prove that Eo = 13.6 eV

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TRE

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1. The problem statement, all variables and given/known data

Verify that the equation of the ground state energy Eo of the Bohr atom: Eo= (2pi2e4mek2)/h2
simplifies to Eo = 13.6 eV. Show clearly how the units of the different
quantities in the equation simplify to the eV.

This is all they give. Nothing more.



2. Relevant equations


Eo= (2pi2e4mek2)/h2



3. The attempt at a solution

me = 9.10938291 x 10-19 Kg

k = 1.3806488 x 10-23J/K

h = 6.62606957 x 10-34J.s

1.6 x 10-19J = 1 eV

2 pi2 = 19.7392088


e4 = 6.589333674 x 10-76 C4

k2 = 1.906195527 x 10-46J2/K2

h2 = 4.390478986 x 10-67J2.s2

when you multiply the above constants together : 2pi2.e4.me.k2 = 0 which means that the whole equation is equal to zero thus Eo = 0 and clearly Eo is not equal to 0 but to 13.6 eV

Also for the units I obtain for the answer when I multiply together and then divide is (C4.Kg/(K2.s2) which is not correct and I did not see any other units for the constants we have to use.
 

Simon Bridge

Science Advisor
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when you multiply the above constants together : 2pi2.e4.me.k2 = 0
Does that make sense mathematically:
How can you multiply a lot of non-zero numbers together and get zero?

Perhaps your calculator has rounded off?
How should you go about multiplying very small numbers - hint: exploit the scientific notation.
 

Simon Bridge

Science Advisor
Homework Helper
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Sorry you feel that way ... and yes, I have done this myself. Many times.

You have clearly made a mistake in the arithmetic since it is not possible to multiply a bunch of non-zero numbers together and get zero for the answer. If it is not a matter of your calculator deciding that 10^-70 or whatever is zero, then it is something else.

GO through the calculation carefully and see which step gets you the zero.

Note: if the dimensions do not match, then the equation is wrong.
 

ehild

Homework Helper
15,287
1,712
1. The problem statement, all variables and given/known data

Verify that the equation of the ground state energy Eo of the Bohr atom: Eo= (2pi2e4mek2)/h2
simplifies to Eo = 13.6 eV. Show clearly how the units of the different
quantities in the equation simplify to the eV.


2. Relevant equations


Eo= (2pi2e4mek2)/h2



3. The attempt at a solution

me = 9.10938291 x 10-19 Kg
there is a mistake here: me = 9.10938291 x 10-31kg.

[STRIKE]k = 1.3806488 x 10-23J/K[/STRIKE]
That 'k' is not the Boltzmann constant, but the constant ke in Coulomb's Law: ke=8.9875 Nm2C-2 .

h = 6.62606957 x 10-34J.s

e=1.6 x 10-19[STRIKE]J = 1 eV[/STRIKE]
You can not replace e with 1 eV. eV is energy, e is charge. e=1.6 x 10-19 C and 1 eV= 1.6 x 10-19 J.

When you multiply the constants, you get the energy in Joules. You have to convert it to eV-s by dividing it 1.6x 10-19 J/eV

Do not forget to set your calculator to SCI mode, to use the normal form of numbers.

ehild
 

TRE

3
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To ehild

Thank You very much for your help, I appreciate it. I finally understand where I went wrong.

Regards
 

ehild

Homework Helper
15,287
1,712
You are welcome.

Just a hint: when you have to calculate with very big or very small numbers, treat the exponents separately, add and subtract them.

ehild
 

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