What is the wavelength of the light?

In summary, the conversation discusses the calculation of the wavelength of light emitted when an electron in a one-dimensional box transitions from the n = 7 state to the n = 6 state. The correct equation for this calculation is provided and it is suggested to check for any errors in the initial calculation.
  • #1
atsum
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Calculate the wavelength of the light emitted when an electron in a one-dimensional box of length 5.2nm makes a transition from the n = 7 state to the n = 6 state.
Express your answer with the appropriate units.

I calculated in this way:
E = n^2*h^2/8*m*a^2
E= (7^2-6^2)*(6.626*10^-34)^2/8*(9.1*10^-31)*(5.2*10^-9)^2
E= 2.9*10^-20 J

E = hc/λ
λ = 6.85*10^-6 m

But the answer is wrong.

What is wrong with my calculation?
 
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  • #2
How do you know the answer is wrong?

It can help if you do the algebra first, then use more convenient units:$$\lambda=\frac{8(m_e c^2) L^2}{hc}\frac{1}{n_f^2-n_i^2}$$

##hc=1.240\text{eV$\mu$m}##
##m_ec^2=511\text{eV}##
##L=0.0052\text{$\mu$m}##
... give it a go.
(Don't forget to check my algebra to get that equation.)
 
  • #3
Simon Bridge said:
How do you know the answer is wrong?

It can help if you do the algebra first, then use more convenient units:$$\lambda=\frac{8(m_e c^2) L^2}{hc}\frac{1}{n_f^2-n_i^2}$$

##hc=1.240\text{eV$\mu$m}##
##m_ec^2=511\text{eV}##
##L=0.0052\text{$\mu$m}##
... give it a go.
(Don't forget to check my algebra to get that equation.)

It is the same calculation as mine.
I did the exercise on MasteringChemistry. It only said my answer is wrong.
 
  • #4
But I got a different order of magnitude from you.
Repeat the calculation ... you have misplaced a decimal point someplace.
 
  • #5


Your calculation is incorrect because you have used the energy formula for a three-dimensional box (E = n^2*h^2/8*m*a^2) instead of the correct formula for a one-dimensional box (E = n^2*h^2/8*m*L^2). The length (L) in the one-dimensional formula represents the length of the box (5.2nm), not the width (a) as in the three-dimensional formula.

Using the correct formula, the energy of the transition would be:
E = (7^2-6^2)*(6.626*10^-34)^2/8*(9.1*10^-31)*(5.2*10^-9)^2 = 8.5*10^-21 J

Then, using the equation E = hc/λ, we can solve for the wavelength:
λ = hc/E = (6.626*10^-34)*(3*10^8)/(8.5*10^-21) = 2.4*10^-7 m

Therefore, the wavelength of the light emitted when an electron in a one-dimensional box of length 5.2nm makes a transition from the n = 7 state to the n = 6 state is 0.24 micrometers (or 240 nanometers).
 

1. What is the definition of wavelength of light?

The wavelength of light is the distance between two consecutive peaks or troughs of a wave. It is typically measured in meters (m) or nanometers (nm).

2. How is the wavelength of light related to color?

The wavelength of light is directly related to the color of light. Shorter wavelengths correspond to colors such as blue and purple, while longer wavelengths correspond to colors such as red and orange.

3. What is the range of wavelengths of visible light?

The range of wavelengths of visible light is approximately 400-700 nanometers (nm).

4. How do scientists measure the wavelength of light?

Scientists use a device called a spectrometer to measure the wavelength of light. This device separates light into its different wavelengths and allows for precise measurements.

5. Can the wavelength of light be changed?

Yes, the wavelength of light can be changed. This can be done through processes such as refraction, diffraction, and interference. For example, passing light through a prism can change its wavelength and create a rainbow of colors.

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