Question

Wavelength of $H^{+}$ion with kinetic energy $1.68\, eV$ is

• A. $1.22\, nm$
• B. $0.22 \, nm$
• C. $0.022\, nm$
• D. $0.122 \, nm$

Answer 1

Answer: (C)

Given, kinetic energy of $H^{+}$ion $=1.68 \,eV$
Mass of proton $=1.6726 \times 10^{-27} \,kg$
We calculate, the wavelength of $H^{+}$ion as follows:
$\lambda=\frac{h}{\sqrt{2 E_{m}}}$
Here,
$E=$ kinetic energy,
$m=$ mass of proton
$h=6.62 \times 10^{-34} \,k\,gm ^{2} \,s ^{-1}$
$=\frac{6.62 \times 10^{-34}}{\sqrt{2 \times 1.67 \times 10^{-27} \times E}}$
$=\frac{0.286}{\sqrt{E(e V)}} \,\mathring{A}=\frac{0.286}{\sqrt{1.68}} \,\mathring{A}=0.220\,\mathring{A}=0.022\, nm$