Question

Calculate the wavelength (in nanometre) associated with a proton moving at $1\times {10}^3$ $m$ ${sec}^{-1}$.
[mass of proton $=1.67\times {10}^{-27}kg$, $h=6.63\times {10}^{-34}J$ $sec$]

• A. $0.032$ nm
• B. $0.40$ nm
• C. $2.5$ nm
• D. $14$ nm

Answer 1

Answer: (B)

$0.40$ nm

$Explanation:$

According to $De-Broglietheorem$ for wavelength:

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

where,

$\lambda =$Wavelength$=?$

$h=$Planck's constant$=6.63\times {10}^{-34}Js$

$m=$Mass of the photon$=1.67\times {10}^{-27}kg$

$v=$Velocity $=1\times {10}^{3}m/s$

$\lambda =\frac{h}{mv}=\frac{6.63\times {10}^{-34}}{1.67\times {10}^{-27}\times 1\times {10}^3}$

$\Rightarrow \lambda =0.40\times {10}^{-9}m=0.40nm$

$\lambda =0.40nm$

$Hencetthecorrectanswerisoption\left(B\right).$