# Calculate Longest & Shortest Wavelength?

• P1nkButt3rflys
In summary, electrons accelerated by a potential difference of 13.14 V pass through a gas of hydrogen atoms at room temperature. The shortest wavelength of light emitted corresponds to a transition from the electron's energy level to the lowest hydrogen energy level. To calculate the longest wavelength, we need to determine the maximum amount of energy lost, which would be a transition from the electron's energy level to the highest energy level available in the hydrogen atom. However, this cannot be determined without more information about the setup and other factors such as Bremsstrahlung.
P1nkButt3rflys
Electrons accelerated by a potential difference of 13.14 V pass through a gas of hydrogen atoms at room temperature.

A) Calculate the wavelength of light emitted with the longest possible wavelength.

B) Calculate the wavelength of light emitted with the shortest possible wavelength.

I've solved part B, but cannot solve part A. Any suggestions?

Part B [CORRECT]
V=13.14V so KE=13.14 eV

En=-13.6/(n^2)
E1= -13.6 eV

E= -13.6 eV + 13.14 eV
E= -0.45 eV

E2= -3.4 eV
E3= -1.5 eV
E4= -0.85 eV
E5= -0.544 eV
E6= -0.378 eV

E=E5-E1
E=(-0.544)-(-13.6)
E= 13.056eV * 1.6e-19 J
E= 2.089e-18 J

E=hc/λ
λ=hc/E
λ=(6.626e-34)*(3e8)/(2.089e-18)
λ= 9.52e-8 m Attempt at Part A) [INCORRECT]

Longest wavelength is in Paschen series (n=3)
E=E4-E3
E=(-0.85)-(-1.5)
E= 0.65eV * 1.6e-19 J
E= 1.04e-19 J

E=hc/λ
λ=hc/E
λ=(6.626e-34)*(3e8)/(1.04e-19)
λ= 1.91e-6 m

The Paschen Lyman and Balmer series are not the only ones available.
Anyway, why choose E4-E3, why not E9-E8 ... isn't that a longer wavelength?
What about the energy lost getting to E9 or E4 or whatever?

The shortest wavelength emmitted corrsponds to the maximum amount of energy lost ... that would be a transition from E (the electron energy) to E0 (the lowest hydrogen energy level).

This you know.

By the same argument:
The longest wavelength emmitted corresponds to the _______ amount of energy lost ... that would be a transition from E (the electron energy) to E__ (the ________ hydrogen energy level).

Fill in the gaps.

------------------------------

note: this assumes the electron gets captured in one go via an electric dipole interaction ... there are other ways to get radiation out of that setup: i.e. Bremsstrahlung

Last edited:

## 1. What is the formula for calculating longest and shortest wavelength?

The formula for calculating longest and shortest wavelength is: λ = c/f, where λ is the wavelength, c is the speed of light (3 x 10^8 m/s), and f is the frequency in hertz (Hz).

## 2. How do you determine the longest and shortest wavelength from a given frequency?

To determine the longest and shortest wavelength from a given frequency, you can use the formula λ = c/f. Simply plug in the frequency in hertz (Hz) and solve for λ. The resulting value will be the longest and shortest wavelength in meters (m).

## 3. Can the longest and shortest wavelength have the same value?

No, the longest and shortest wavelength cannot have the same value. This is because the wavelength and frequency have an inverse relationship, meaning that as one increases, the other decreases. Therefore, the longest and shortest wavelength will always have different values.

## 4. What is the difference between longest and shortest wavelength?

The longest and shortest wavelength refer to the two extremes of the electromagnetic spectrum. The longest wavelength is associated with radio waves, while the shortest wavelength is associated with gamma rays. The main difference between them is their frequency, with radio waves having a lower frequency and gamma rays having a higher frequency.

## 5. How is the longest and shortest wavelength used in science?

The longest and shortest wavelength are used in various scientific fields, such as astronomy, physics, and chemistry. In astronomy, the longest and shortest wavelengths are used to study the properties of celestial objects, while in physics and chemistry, they are used to understand the behavior of matter and interactions between particles. They are also used in telecommunications and other technological applications.

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