Calculating the Kinetic Energy and De Broglie Wavelength of an Ejected Electron

In summary, to calculate the kinetic energy of an ejected electron, use the formula KE = 1/2 * m * v^2, where m is the mass and v is the velocity of the electron. The De Broglie wavelength of an ejected electron is calculated using the formula λ = h / p, where h is Planck's constant and p is the momentum of the electron. The kinetic energy and De Broglie wavelength are inversely proportional, meaning as one increases, the other decreases. Both can be measured experimentally using an electron spectrometer. Knowing these values is important for understanding the behavior of matter at the quantum level and has various applications in fields such as quantum mechanics, particle physics, and materials science.
  • #1
thursdaytbs
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If 15eV photon interacts with a Hydrogen atom at groundstate [-13.6eV], and all 15eV is transferred to the atom. How would the KE of the ejected electron be found? and what is the de Broglie wavelength of the electron?

For the Kinetic Energy, i said 15eV = KE + 13.6eV, KE = 1.4eV

for the wavelength, i have no clue. any help?
 
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  • #2
The de Broglie wavelength is found by dividing Planck's constant by the momentum of the moving object. You can find the momentum using the kinetic energy.
 
  • #3


To find the kinetic energy of the ejected electron, we can use the equation KE = hf - BE, where KE is the kinetic energy, hf is the energy of the incident photon (15eV in this case), and BE is the binding energy of the electron in the ground state (-13.6eV for Hydrogen). Plugging in the values, we get KE = 15eV - (-13.6eV) = 1.4eV. This means that the ejected electron will have a kinetic energy of 1.4 electron volts.

To find the de Broglie wavelength of the electron, we can use the equation λ = h/p, where λ is the de Broglie wavelength, h is Planck's constant (6.626 x 10^-34 joule seconds), and p is the momentum of the electron. The momentum of the electron can be calculated using the equation p = √(2mKE), where m is the mass of the electron (9.109 x 10^-31 kg) and KE is the kinetic energy we calculated earlier (1.4eV).

Plugging in the values, we get p = √(2(9.109 x 10^-31 kg)(1.4eV)(1.602 x 10^-19 J/eV)) = 1.48 x 10^-24 kg m/s. Now, we can use this value to calculate the de Broglie wavelength: λ = (6.626 x 10^-34 joule seconds)/(1.48 x 10^-24 kg m/s) = 4.47 x 10^-10 meters. Therefore, the de Broglie wavelength of the ejected electron is 4.47 x 10^-10 meters.
 

Related to Calculating the Kinetic Energy and De Broglie Wavelength of an Ejected Electron

1. How do you calculate the kinetic energy of an ejected electron?

To calculate the kinetic energy of an ejected electron, you can use the formula KE = 1/2 * m * v^2, where m is the mass of the electron and v is its velocity. The mass of an electron is a constant value of 9.11 x 10^-31 kg and its velocity can be measured using an electron spectrometer.

2. What is the De Broglie wavelength of an ejected electron?

The De Broglie wavelength of an ejected electron is a physical property that describes the wave-like behavior of particles, including electrons. It is calculated using the formula λ = h / p, where λ is the De Broglie wavelength, h is Planck's constant (6.626 x 10^-34 J*s), and p is the momentum of the electron.

3. How does the kinetic energy of an ejected electron relate to its De Broglie wavelength?

According to the De Broglie wavelength equation, the wavelength of a particle is inversely proportional to its momentum. This means that as the kinetic energy of an ejected electron increases, its momentum and therefore its De Broglie wavelength decreases. This relationship is known as the wave-particle duality of matter.

4. Can the kinetic energy and De Broglie wavelength of an ejected electron be measured experimentally?

Yes, both the kinetic energy and De Broglie wavelength of an ejected electron can be measured experimentally using an electron spectrometer. The spectrometer allows for the measurement of the electron's velocity, which can then be used to calculate its kinetic energy. The De Broglie wavelength can also be determined by measuring the electron's diffraction pattern.

5. Why is it important to calculate the kinetic energy and De Broglie wavelength of an ejected electron?

Calculating the kinetic energy and De Broglie wavelength of an ejected electron is important for understanding the behavior of matter at the quantum level. It helps to explain the wave-like properties of particles and how they interact with their environment. This information is crucial for various applications in fields such as quantum mechanics, particle physics, and materials science.

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