Answer:
The wavelength of electron is 357256.63 times more than that of gold atom travelling at same speed.
Explanation:
The de-broglie wavelength is obtained using the formula
[tex]\lambda =\frac{h}{mv}[/tex]
For an electron we have
[tex]m=9.11\times 10^{-31}kg[/tex]
[tex]v=0.01c=0.01\times 3\times 10^{8}m/s=3\times 10^{6}m/s[/tex]
Using these values in the relation we get
[tex]\lambda _{electron)=\frac{6.62\times 10^{-34}}{9.11\times 10^{-31}\times 3\times 10^{6}}[/tex]
[tex]\therefore \lambda _{electron}=242.22\times 10^{-12}m[/tex]
For a gold atom we have
[tex]m=3.27\times 10^{-25}kg[/tex]
[tex]v=0.01c=0.01\times 3\times 10^{8}m/s=3\times 10^{6}m/s[/tex]
Using these values in the relation we get
[tex]\lambda _{gold)=\frac{6.62\times 10^{-34}}{3.27\times 10^{-25}\times 3\times 10^{6}}[/tex]
[tex]\therefore \lambda _{gold}=6.748\times 10^{-16}m[/tex]
thus we can write
[tex]\frac{\lambda _{electron}}{\lambda _{gold}}=\frac{242.22\times 10^{-12}}{6.748\times 10^{-16}}=357256.63[/tex]
