This problem is killing me [calculation of electron transition]

In summary, the problem is killing me! The value of n_i for an electron that emits a photon of wavelength 93.14 nm when it returns to the ground state in the H atom is 0.7.
  • #1
eq123
6
0
this problem is killing me! [calculation of electron transition]

i've been trying to solve this problem.. the answer should be 7.. my answer is 0.7 !

What is the value of n_i for an electron that emits a photon of wavelength 93.14 nm when it returns to the ground state in the H atom?

my solution..

n_f=1
λ=93.14 nm×(10^(-9) m)/(1 nm)=93.14×10^(-9) m
∆E=hν=hc/λ=(6.63×10^(-34)×3.00×10^8)/(93.14×10^(-9))≈2.14×10^(-18)
∆E=-2.18×10^(-18) (1/(n_f^2 )-1/(n_i^2 ))
2.14×10^(-18)=-2.18×10^(-18) (1/1^2 -1/(n_i^2 ))
-2.14/2.18=1-1/(n_i^2 )
1.982= 1/(n_i^2 )
n_i^2=0.5045
n_i=√0.5045≈0.7

n_i = n initial
n_f = n final
λ = wavelength ( lambda )
∆E = energy of the transition
h = plank's constant
ν = frequency ( nu )
c = speed of light

if reading the solution is an issue.. just past it in microsoft word and activate the equation mode..
 
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  • #2


eq123 said:
if reading the solution is an issue.. just past it in microsoft word and activate the equation mode..

We have something called LaTeX for such situations. And I don't have, use, nor want to use Microsoft Word.

When I solve

[tex]\frac 1 {93.14nm} = R_{\infty} (\frac 1 {1^2} - \frac 1 {n^2})[/tex]

for n, I get 6.85 - close enough to 7. No idea what is 2.18x10-18, as far as I can tell Rydberg constant is 1.097x107 m-1.

--
methods
 
  • #3


Borek said:
for n, I get 6.85 - close enough to 7. No idea what is 2.18x10-18, as far as I can tell Rydberg constant is 1.097x107 m-1.

2.18x10-18 is the Rhydberg constant in joules.
 
  • #4


OK, I know what have happened. Check your math, you made a simple error when solving.

--
methods
 
  • #5


i already figured it out.. since the electron is returning to its ground state.. it is releasing energy.. which means that ∆E is negative.. after taking that into consideration.. the answer should be 7..

2.18x10-18 is the Rhydberg constant in joules.
wow.. it makes more sense to me now!

thank you.
 

What is electron transition?

Electron transition is the movement of an electron from one energy level to another within an atom. This can occur when an electron absorbs or emits energy.

Why is calculating electron transition important?

Calculating electron transition is important because it helps us understand and predict the behavior of atoms and molecules. It also plays a crucial role in fields such as chemistry, physics, and materials science.

How is electron transition calculated?

Electron transition is calculated using the principles of quantum mechanics. This involves solving mathematical equations to determine the energy levels of electrons in an atom or molecule.

What factors affect electron transition?

The factors that affect electron transition include the energy of the incoming or outgoing photon, the energy levels of the electrons involved, and the physical properties of the atom or molecule.

What are some applications of electron transition calculations?

Some applications of electron transition calculations include understanding the absorption and emission of light by atoms and molecules, determining the electronic structure of materials, and studying chemical reactions.

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