Answer:
Part A:
For electron:
[tex]\lambda_e=2.1392*10^{-10} m[/tex]
For Proton:
[tex]\lambda_p=1.16696*10^{-13} m[/tex]
Part B:
For electron:
[tex]\lambda_e=9.44703*10^{-12} m[/tex]
For Proton:
[tex]\lambda_p=2.20646*10^{-13} m[/tex]
Explanation:
Formula for wave length λ is:
[tex]\lambda=\frac{h}{mv}[/tex]
where:
h is Planck's constant=[tex]6.626*10^{-34}[/tex]
m is the mass
v is the velocity
Part A:
For electron:
[tex]\lambda_e=\frac{6,626*10^{-34}}{(9.11*10^{-31})*(3.4*10^6)} \\\lambda_e=2.1392*10^{-10} m[/tex]
For Proton:
[tex]\lambda_p=\frac{6,626*10^{-34}}{(1.67*10^{-27})*(3.4*10^6)} \\\lambda_p=1.16696*10^{-13} m[/tex]
Wavelength of proton is smaller than that of electron
Part B:
Formula for K.E:
[tex]K.E=\frac{1}{2}mv^2\\v=\sqrt{2 K.E/m}[/tex]
For Electron:
[tex]v_e=\sqrt{\frac{2*2.7*10^{-15}}{9.11*10^{-31}}} \\v_e=76990597.74\ m/s[/tex]
Wavelength for electron:
[tex]\lambda_e=\frac{6,626*10^{-34}}{(9.11*10^{-31})*(76990597.74)} \\\lambda_e=9.44703*10^{-12} m[/tex]
For Proton:
[tex]v_p=\sqrt{\frac{2*2.7*10^{-15}}{1.67*10^{-27}}} \\v_p=1798202.696\ m/s[/tex]
Wavelength for proton:
[tex]\lambda_p=\frac{6,626*10^{-34}}{(1.67*10^{-27})*(1798202.696)} \\\lambda_p=2.20646*10^{-13} m[/tex]
Wavelength of electron is greater than that of proton.
