Question

Calculate the wavelength (in nanometer) associated with a proton moving at $1.0\times {10}^{3}m{s}^{-1}$
$(\text{Mass of proton}=1.67\times {10}^{-27}kg$)
$\left(\text{Planck's constant}\right(h)=6.63\times {10}^{-34}Js)$

• A. 0.40 nm
• B. 1.5 nm
• C. 10.0 nm
• D. 2.3 nm

Answer 1

The correct option is A 0.40 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 $=1000m/s$
Substituting the values,
$\lambda =\frac{6.63\times {10}^{-34}}{1.67\times {10}^{-27}\times 1000}$
$=3.97\times {10}^{-10}m$
$=0.397nm\approx 0.40nm$