Question

The speed of a proton is one hundredth of the speed of light in vacuum. What is its De-Broglie wavelength? Assume that one mole of protons has a mass equal to one gram. [h = 6.626x10^-27 erg sec]

Answer 1

speed of proton(v)=speed of light/100

v=3 x 10^6m/sec

now
De-Broglie wavelength=h/mv

=(6.626 x 10^-34)/(1.67 x 10^-27 x3 x 10^6)

=(6.626/3x1.67) x 10^-34+21

=1.33 x 10^-13 m (approx)

Answer 2

Answer:

$1.33\times 10^{-13} m$ is its De-Broglie wavelength

Explanation:

De-Broglie wavelength is calculated by using the formula:

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

where,

h = Planck's constant = $6.6\times 10^{-34}Js$

m = mass of a proton

1 mole of proton = 1 g

Mass of $6.022\times 10^{23} protons =1 g$

Mass of 1 proton = $m=\frac{1}{6.022\times 10^{23} g=0.1660\times 10^{-26} kg$

v = velocity of proton

$v=\frac{1}{100}\times c=\frac{1}{100}\times 3\times 10^8 m/s =3\times 10^6 m/s$

$\lambda=\frac{h}{mv}=\frac{6.626x10^{-34} J sec}{0.1660\times 10^{-26} kg\times 3\times 10^6 m/s}$

$\lambda =1.33\times 10^{-13} m$

$1.33\times 10^{-13} m$ is its De-Broglie wavelength