Electron and wavelength problem

In summary, the problem involves an electron on the n=6 energy level emitting a wavelength of 410.2nm. To determine the energy level it moves to, the equation 1/L = R(1/N^2 - 1/n^2) is used, where N is the initial lower level and n is the final upper level. Plugging in the values, we get 1/410.2nm = 1.096779*10^7 m^-1 (1/36 - 1/n^2). After solving for the term within the parenthesis, we must add 1/36 to it before taking the square root. This gives us a value of approximately 6 for the final energy level,
  • #1
David112234
105
3

Homework Statement


Electron on n=6 level emits wavelength of 410.2nm.
What energy level does it move too?

Homework Equations


1/L = R ( 1/N^2 - 1/n^2)
where N is initial and n final
R=1.096779*10^7 m

The Attempt at a Solution


1/410.2 = 10967790 (1/36 - 1/n^2)
1/4498975152 = (1/36 - 1/n^2)
-1/36 -1/36
4498975152 =n^2
sqrt
n=67074...
this number is wrong, it is not an energy level, and not one of the answers, what did I do wrong?
 
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  • #2
David112234 said:
1/L = R ( 1/N^2 - 1/n^2)
where N is initial and n final
Careful here. N is the lower level and n is the upper level, not necessarily initial and final.

Put the units in your equation, you will see where it went wrong.
 
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  • #3
DrClaude said:
Careful here. N is the lower level and n is the upper level, not necessarily initial and final.

Put the units in your equation, you will see where it went wrong.
alright,
R is in m^-1
and L is in nm,

so it will be .0000004102m*10967760m^-1 = .449897515 m/m
Now I add 36 and take the sqrt, which gives me a number slightly larger than 6, which still is not correct. Did I miss other units?
 
  • #4
David112234 said:
so it will be .0000004102m*10967760m^-1 = .449897515 m/m
Almost. I think it is simpler to make calculation using powers of 10 (less chance of an error):
410.2×10-9 m × 1.096779×107 m-1 = ?

David112234 said:
Now I add 36 and take the sqrt
You can't do that,
$$
\frac{1}{a} + \frac{1}{b} \neq \frac{1}{a+b}
$$
You need to add 1/36 to 1 over the number you will get for λ×R.
 
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  • #5
DrClaude said:
Almost. I think it is simpler to make calculation using powers of 10 (less chance of an error):
410.2×10-9 m × 1.096779×107 m-1 = ?You can't do that,
$$
\frac{1}{a} + \frac{1}{b} \neq \frac{1}{a+b}
$$
You need to add 1/36 to 1 over the number you will get for λ×R.

I thought since all the terms were under 1 that I could just solve the denominators, like this property

X(2x+5) = x14
2x+5= 14

also, how do you display fractions on this forum like you did?
 
  • #6
David112234 said:
I thought since all the terms were under 1 that I could just solve the denominators, like this property

X(2x+5) = x14
2x+5= 14
That makes use of the properties of the logarithm
$$
\begin{align*}
x^a &= x^b \\
\log(x^a) &= \log(x^b) \\
a \log(x) &= b \log(x) \\
a &= b
\end{align*}
$$
It doesn't work for ##a^{-1} + b^{-1}##.

David112234 said:
also, how do you display fractions on this forum like you did?
I used the Latex capabilities of PF. See https://www.physicsforums.com/help/latexhelp/ for more info.
 
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  • #7
DrClaude said:
That makes use of the properties of the logarithm
$$
\begin{align*}
x^a &= x^b \\
\log(x^a) &= \log(x^b) \\
a \log(x) &= b \log(x) \\
a &= b
\end{align*}
$$
It doesn't work for ##a^{-1} + b^{-1}##.I used the Latex capabilities of PF. See https://www.physicsforums.com/help/latexhelp/ for more info.

Thank you. I did it all out and the value I got it .66666, which still does not seem right
 
  • #8
David112234 said:
I did it all out and the value I got it .66666, which still does not seem right
Indeed. I get a nice value. Could you show your calculation?
 

1. What is the electron and wavelength problem?

The electron and wavelength problem is a fundamental concept in quantum mechanics that arises when trying to determine the location of an electron. According to the Heisenberg uncertainty principle, it is impossible to know both the exact position and momentum of an electron at the same time. This creates a problem in determining the wavelength or energy of an electron.

2. How does the electron and wavelength problem relate to the wave-particle duality of electrons?

The electron and wavelength problem is closely related to the wave-particle duality of electrons. This duality states that electrons can behave as both particles and waves. When trying to determine the wavelength of an electron, it is necessary to treat it as a wave. However, when measuring its position, it acts as a particle. This duality creates the uncertainty in determining both the position and wavelength of an electron.

3. Can the electron and wavelength problem be solved?

No, the electron and wavelength problem cannot be solved completely. The uncertainty principle is a fundamental law of quantum mechanics and cannot be overcome. However, scientists have developed mathematical models and equations to accurately predict the probability of an electron's position and wavelength at any given time.

4. What are some real-life applications of the electron and wavelength problem?

The electron and wavelength problem has many applications in modern technology, particularly in the field of electronics. For example, the principles of quantum mechanics are essential for the development of transistors and computer chips, which are the building blocks of modern computers. The understanding of the electron and wavelength problem also plays a crucial role in developing advanced medical imaging techniques such as MRI.

5. How does the electron and wavelength problem impact our understanding of the universe?

The electron and wavelength problem, along with other principles of quantum mechanics, has completely revolutionized our understanding of the universe. It has shown that the laws of classical physics do not apply at the subatomic level and that there is a fundamental uncertainty in the behavior of particles. This has led to new theories and breakthroughs in fields such as cosmology and particle physics.

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