Question

(1 points) Find the wavelength of a proton moving at 1.00% of the speed of light. The mass of a proton is 1.67 \times 10^{-27} ~\text{kg}1.67×10 ​−27 ​​ kg.

Answer 1

Answer:

The wavelength of the proton will be $1.33\times 10^{-15}\ m$

Explanation:

Given the speed of the proton is $1.00 \%$ of speed of light.

And the mass of the proton is $1.67 \times 10^{-27}\ kg$..

We need to find the wavelength of moving proton.

As we know the speed of the light $c=2.998\times 10^8\ m/s$

So, speed of the proton will be

$1.00 \%(c)=\frac{1}{100}\times (c)=0.01\times 2.98\times 10^8\ m/s$

Now, we will use De Broglie's Equation to find out wavelength..

$\lambda =\frac{h}{mv}$

Where

$\lambda$ is the wavelength

$h$ is the Planck's constant $6.626\times 10^{-34}\ m^2\ kg / s$

$m$ is the mass in kg

$v$ is the speed in m/s

$\lambda=\frac{6.626\times 10^{-34}}{1.67 \times 10^{-27}\times 0.01\times 2.98\times 10^8}\\ \\\lambda=\frac{6.626}{1.67\times 0.01\times 2.98}\times 10^{-15}\\ \\\lambda=133.14\times 10^{-15}\ m\\\lambda=1.33\times 10^{-15}\ m$

So, the wavelength of the proton will be $1.33\times 10^{-15}\ m$