Question

Calculate the wavelength (in nanometer) associated with a proton moving at $1.0\times {10}^{4}m{s}^{-1}$
$\text{Mass of proton}=1.67\times {10}^{-27}kg$
$\text{Planck's constant}\left(h\right)=6.63\times {10}^{-34}Js$

• A. 0.040 nm
• B. 0.25 nm
• C. 1.4 nm
• D. 0.032 nm

Answer 1

The correct option is A 0.040 nm

According to de-Broglie hypothesis,
$\lambda =\frac{h}{mv}$
where,
h = Planck's constant $=6.63\times {10}^{-34}Js$
m = mass of the object $=1.67\times {10}^{-27}kg$
v = velocity of object $=10000m/s$
Substituting the values,
$\lambda =\frac{6.63\times {10}^{-34}}{1.67\times {10}^{-27}\times 10000}$
$=3.97\times {10}^{-11}m$
$=0.0397nm\approx 0.040nm$