Respuesta :

skyluke89
(a) The electron kinetic energy is
[tex]K=3.00 eV[/tex]
which can be converted into Joule by keeping in mind that
[tex]1 eV=1.6 \cdot 10^{-19}eV[/tex]
So that we find
[tex]K=3.00 eV \cdot 1.6 \cdot 10^{-19} eV/J =4.8 \cdot 10^{-19}J[/tex]

The kinetic energy of the electron is related to its momentum p by:
[tex]K= \frac{p^2}{2m} [/tex]
where m is the electron mass. Re-arranging the equation, we find
[tex]p= \sqrt{ 2Km}= \sqrt{ 2 ( 4.8 \cdot 10^{-19} J)(9.1 \cdot 10^{-31} kg) } =9.35 \cdot 10^{-25} kgm/s [/tex]

And now we can use De Broglie's relationship to find its wavelength:
[tex]\lambda= \frac{h}{p}= \frac{6.6 \cdot 10^{-34} Js}{9.35 \cdot 10^{-25} kg m/s} =7.06 \cdot 10^{-10}m [/tex]
where h is the Planck constant.


(b) By using the same procedure of part (a), we can convert the photon energy into Joules:
[tex]E=3.00 eV \cdot 1.6 \cdot 10^{-19} eV/J =4.8 \cdot 10^{-19}J[/tex]

The energy of a photon is related to its frequency f by:
[tex]E=hf[/tex]
where h is the Planck constant. Re-arranging the equation, we find
[tex]f= \frac{E}{h}= \frac{4.8 \cdot 10^{-19} J}{6.6 \cdot 10^{-34}Js} =7.27 \cdot 10^{14}Hz [/tex]

And now we can use the relationship between frequency f, speed of light c and wavelength [tex]\lambda[/tex] of a photon, to find its wavelength:
[tex]\lambda= \frac{c}{f}= \frac{3 \cdot 10^8 m/s}{7.27 \cdot 10^{14} Hz} =4.13 \cdot 10^{-7} m [/tex]
onyebuchinnaji

The wavelength of the electron from the given kinetic energy is [tex]7.1 \times 10^{-10} \ m[/tex].

The wavelength of the electron from the given photon energy is [tex]4.13 \times 10^{-7} \ m[/tex].

Momentum of the electron

The momentum of the electron is calculated as follows;

[tex]P = \sqrt{2Km} \\\\P = \sqrt{2 \times (3 \times 1.6 \times 10^{-19} \times 9.11 \times 10^{-31} } = 9.35 \times 10^{-25} \ kgm/s[/tex]

Wave of the electron

The wavelength of the electron is determined by using  De Broglie's equation.

[tex]\lambda = \frac{h}{p} \\\\\lambda = \frac{6.6 \times 10^{-34} }{9.35 \times 10^{-25}} = 7.1 \times 10^{-10} \ m[/tex]

Wavelength of the electron from the given photon energy

E = hf

[tex]E = \frac{hc}{\lambda} \\\\\lambda = \frac{hc}{E} \\\\\lambda = \frac{6.6 \times 10^{-34} \times 3\times 10^8}{3\times 1.6 \times 10^{-19}} \\\\\lambda = 4.13 \times 10^{-7} \ m[/tex]

Learn more about wavelength of photons here: https://brainly.com/question/10728818

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