Respuesta :
Explanation:
Given that,
(a) Speed, [tex]v=6.66\times 10^6\ m/s[/tex]
Mass of the electron, [tex]m_e=9.11\times 10^{-31}\ kg[/tex]
Mass of the proton, [tex]m_p=1.67\times 10^{-27}\ kg[/tex]
The wavelength of the electron is given by :
[tex]\lambda_e=\dfrac{h}{m_ev}[/tex]
[tex]\lambda_e=\dfrac{6.63\times 10^{-34}}{9.11\times 10^{-31}\times 6.66\times 10^6}[/tex]
[tex]\lambda_e=1.09\times 10^{-10}\ m[/tex]
The wavelength of the proton is given by :
[tex]\lambda_p=\dfrac{h}{m_p v}[/tex]
[tex]\lambda_p=\dfrac{6.63\times 10^{-34}}{1.67\times 10^{-27}\times 6.66\times 10^6}[/tex]
[tex]\lambda_p=5.96\times 10^{-14}\ m[/tex]
(b) Kinetic energy, [tex]K=1.71\times 10^{-15}\ J[/tex]
The relation between the kinetic energy and the wavelength is given by :
[tex]\lambda_e=\dfrac{h}{\sqrt{2m_eK}}[/tex]
[tex]\lambda_e=\dfrac{6.63\times 10^{-34}}{\sqrt{2\times 9.11\times 10^{-31}\times 1.71\times 10^{-15}}}[/tex]
[tex]\lambda_e=1.18\times 10^{-11}\ m[/tex]
[tex]\lambda_p=\dfrac{h}{\sqrt{2m_pK}}[/tex]
[tex]\lambda_p=\dfrac{6.63\times 10^{-34}}{\sqrt{2\times 1.67\times 10^{-27}\times 1.71\times 10^{-15}}}[/tex]
[tex]\lambda_p=2.77\times 10^{-13}\ m[/tex]
Hence, this is the required solution.
