What is the value of ni for an electron

In summary, the value of ni for an electron that emits a photon of wavelength 93.14 nm when it returns to the ground state in the hydrogen atom is 6.63 x 10^-34.
  • #1
cindy1234
3
0

Homework Statement



what is the value of ni for an electron that emits a photon of wavelength 93.14 nm when it returns to the ground state in the hydrogen atom

Homework Equations



planck's constant 6.63 x 10^-34

The Attempt at a Solution


no idea [/B]
 
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  • #2
Hi cindy1234,

You need to provide some attempt before help can be given. Start by looking though your course notes and text to find relevant equations pertaining to hydrogen emission lines, wavelength and energy, and so forth.
 
  • #3
this is as far as i can get still don't get some of this

change 93.14 nm to meters
93.14 x 1 x 10^-9 = 9.314 x 10^-8

9.314 x 10^-8 = 1.097 x 10^7 rydberg constant

1 - 1 / n exponent 2 subscript 2 = 0.9787 (how did they get this)
 
  • #4
There's a particular formula that applies here that should be in your notes or text. It's probably in the chapter that introduces quantum theory as it pertains to atoms and light emission/absorption. Hint: the constant that you named above is used in the formula of the same name.
 
  • #5
chemistry text - has only one example of an electron transition - that is calculate the wavelength in nm of the photon emitted when an electron transitions from the n = 4 state to the n = 2 state in a hydrogen atom - which i can do but i don't know how to change this to get the n subscript i

tried changing to m and 1 / 9.314 x 10^-8 and get 1.074 x 10^7 as an answer

found the following on the internet
wavelength = 430 nm
find n i
(1/n 1 ^2 - 1 / n 2 ^2) = 2325581 / (1.09677581 x 10^7)
(1/2^2 - 1/n2^2) = 0.212038
1/n2^2 = 0.25 - 0.212038
n2^2 = 26.342 (only part i don't understand) (only need help with this part)
n^2 = 5 (square root)
 
Last edited:
  • #6
cindy1234 said:
chemistry text - has only one example of an electron transition - that is calculate the wavelength in nm of the photon emitted when an electron transitions from the n = 4 state to the n = 2 state in a hydrogen atom - which i can do but i don't know how to change this to get the n subscript i
Concentrate on finding the value for the ##n_i## rather than its subscript. You know the sequence of integers that the n's are drawn from, so you can later match the value of n to a subscript.
tried changing to m and 1 / 9.314 x 10^-8 and get 1.074 x 10^7 as an answer

found this on internet
change nm to m 93.14 nm to 9.314 x 10^-8 m

1 - 1 / exponent 2 n subscript 2 = 0.9787 (how did they get this)
1/ exponent 2 n subscript 2 = 0.02128 (how did they get this)
n exponent 2 subscript 2 = 46.98 (how did they get this)
n subscript 2 = 6.85 rounded to 7 (square root of 46.98)
They started with the Rydberg formula (which your chemistry text should have). Your problem statement states that the electron transitions to the ground state, giving you one of the n values. The other n value is then the unknown that you're looking for.

Note that you can use the x2 and x2 buttons in the edit window top bar menu to create subscripts and superscripts for your formulas.
 
  • #7
cindy1234 said:
found the following on the internet
wavelength = 430 nm
find n i
(1/n 1 ^2 - 1 / n 2 ^2) = 2325581 / (1.09677581 x 10^7)
(1/2^2 - 1/n2^2) = 0.212038
1/n2^2 = 0.25 - 0.212038
n2^2 = 26.342 (only part i don't understand) (only need help with this part)
Both sides were inverted:

(1/n2^2)-1 = (0.25 - 0.212038)-1
n2^2 = (0.037962)-1
n2^2 = 26.342
n2 = √26.342
n2 ≈ 5
 

Related to What is the value of ni for an electron

1. What is the value of ni for an electron?

The value of ni for an electron, also known as the intrinsic carrier concentration, varies depending on the material. For silicon, the most commonly used semiconductor material, the value is approximately 1.5 x 10^10 per cubic centimeter at room temperature.

2. Why is ni important in semiconductor materials?

Ni is important because it represents the balance between the number of electrons and holes in a material. At this equilibrium point, the material is considered intrinsic, meaning it has no impurities. This is necessary for proper functioning of semiconductor devices.

3. How does the value of ni change with temperature?

The value of ni increases with temperature, as more thermal energy is available to generate electron-hole pairs. This is known as the temperature dependence of ni and is an important factor in the performance of semiconductor devices.

4. What factors can affect the value of ni in a material?

The value of ni can be affected by the type and concentration of impurities in a material, as well as the material's crystal structure and temperature. It can also be controlled through processes such as doping, which introduces impurities to modify the material's conductivity.

5. How is the value of ni determined experimentally?

The value of ni can be determined experimentally through various methods, such as Hall effect measurements, optical absorption spectroscopy, and capacitance-voltage measurements. These techniques can provide information about the material's carrier concentration and mobility, which can then be used to calculate the value of ni.

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