Respuesta :
Answer:
(a). The wave length of 1 eV electron is [tex]1.23\times10^{-9}\ m[/tex].
(b). The wave length of 10 MeV proton is [tex]9.06\times10^{-15}\ m[/tex].
(c). The wave length of 100 MeV electron is [tex]1.23\times10^{-13}\ m[/tex].
Explanation:
Given that,
[tex]E =1\ ev[/tex]
[tex]E=10 MeV[/tex]
[tex]E=100 MeV[/tex]
(a). We need to calculate the wavelength of 1 eV electron
Using formula of De Broglie wavelength
[tex]\lambda=\dfrac{h}{\sqrt{2mE}}[/tex]
[tex]\lambda=\dfrac{6.63\times10^{-34}}{\sqrt{2\times9.1\times10^{-31}\times1\times1.6\times10^{-19}}}[/tex]
[tex]\lambda=1.23\times10^{-9}\ m[/tex]
[tex]\lambda=1.23\ nm[/tex]
The wave length of 1 eV electron is [tex]1.23\times10^{-9}\ m[/tex].
(b). We need to calculate the wavelength of 10 MeV proton
Using formula of De Broglie wavelength
[tex]\lambda=\dfrac{h}{\sqrt{2mE}}[/tex]
Put the value into the formula
[tex]\lambda=\dfrac{6.63\times10^{-34}}{\sqrt{2\times1.67\times10^{-27}\times10\times10^{6}\times1.6\times10^{-19}}}[/tex]
[tex]\lambda=\dfrac{6.63\times10^{-34}}{\sqrt{5.344\times10^{-39}}}[/tex]
[tex]\lambda=9.06\times10^{-15}\ m[/tex]
The wave length of 10 MeV proton is [tex]9.06\times10^{-15}\ m[/tex].
(c). We need to calculate the wavelength of 100 MeV electron
Using formula of De Broglie wavelength
[tex]\lambda=\dfrac{h}{\sqrt{2mE}}[/tex]
Put the value into the formula
[tex]\lambda=\dfrac{6.63\times10^{-34}}{\sqrt{2\times9.1\times10^{-31}\times100\times10^{6}\times1.6\times10^{-19}}}[/tex]
[tex]\lambda=1.23\times10^{-13}\ m[/tex]
The wave length of 100 MeV electron is [tex]1.23\times10^{-13}\ m[/tex].
Hence, This is the required solution.
