Answer:
The wavelength of the proton will be [tex]1.33\times 10^{-15}\ m[/tex]
Explanation:
Given the speed of the proton is [tex]1.00 \%[/tex] of speed of light.
And the mass of the proton is [tex]1.67 \times 10^{-27}\ kg[/tex]..
We need to find the wavelength of moving proton.
As we know the speed of the light [tex]c=2.998\times 10^8\ m/s[/tex]
So, speed of the proton will be
[tex]1.00 \%(c)=\frac{1}{100}\times (c)=0.01\times 2.98\times 10^8\ m/s[/tex]
Now, we will use De Broglie's Equation to find out wavelength..
[tex]\lambda =\frac{h}{mv}[/tex]
Where
[tex]\lambda[/tex] is the wavelength
[tex]h[/tex] is the Planck's constant [tex]6.626\times 10^{-34}\ m^2\ kg / s[/tex]
[tex]m[/tex] is the mass in kg
[tex]v[/tex] is the speed in m/s
[tex]\lambda=\frac{6.626\times 10^{-34}}{1.67 \times 10^{-27}\times 0.01\times 2.98\times 10^8}\\ \\\lambda=\frac{6.626}{1.67\times 0.01\times 2.98}\times 10^{-15}\\ \\\lambda=133.14\times 10^{-15}\ m\\\lambda=1.33\times 10^{-15}\ m[/tex]
So, the wavelength of the proton will be [tex]1.33\times 10^{-15}\ m[/tex]
