Respuesta :
Answer:
The energy and the wavelength of the photon are 1.546 MeV and [tex]8.036\times10^{-13}\ m[/tex].
Explanation:
Given that,
Kinetic energy = 261 KeV
Planck's constant [tex]h = 6.626\times10^{−34}\ J.s[/tex]
Speed of light [tex]c=2.998\times10^{8}\ m/s[/tex]
Mass of electron [tex]m_{e}=9.109\times10^{-31}\ kg[/tex]
Charge [tex]q=1.602\times10^{-19}\ C[/tex]
(A). We need to calculate the energy of the photon
Using formula of rest mass energy
[tex]E=m_{0}c^2[/tex]
[tex]E=9.109\times10^{-31}\times(3\times10^{8})^2[/tex]
[tex]E=8.198\times10^{-14}\ J[/tex]
Energy in eV
[tex]E=\dfrac{8.198\times10^{-14}}{1.6\times10^{-19}}[/tex]
[tex]E=512375\ eV[/tex]
[tex]E=0.512\ MeV[/tex]
The total energy of photon
[tex]TE=2(E+K.E)[/tex]
[tex]TE=2(0.512+0.261)[/tex]
[tex]TE=1.546\ MeV[/tex]
(B). We need to calculate the wavelength of the photon
Using formula of wavelength
[tex]\lambda=\dfrac{hc}{E}[/tex]
Put the value into the formula
[tex]\lambda=\dfrac{6.626\times10^{−34}\times3\times10^{8}}{1.546\times10^{6}\times1.6\times10^{-19}}[/tex]
[tex]\lambda=8.036\times10^{-13}\ m[/tex]
Hence, The energy and the wavelength of the photon are 1.546 MeV and [tex]8.036\times10^{-13}\ m[/tex].
