Question

A hydrogen molecule at ${200}^{o}C$ moves at a velocity of $2.2\times {10}^{5}cm/sec$. Its De-Broglie was length is in order:

• A. ${10}^4{A}^o$
• B. $1A^o$
• C. ${10}^3{A}^o$
• D. $10A^o$

Answer 1

The correct option is C ${10}^3{A}^o$

De-broglie wavelength of an electron is given by $\lambda =\frac{h}{mv}$

Here substituting $m=9.1\times {10}^{-31}kg$, $v=2.2\times {10}^{5}cm/s=2.2\times {10}^{3}m/s$ and $h=6.63\times {10}^{-34}Js$

Therefore $\lambda =\frac{6.63\times {10}^{-34}Js}{(9.1\times {10}^{-31}kg)(2.2\times {10}^{3}m/s)}$

$\lambda =0.3282\times {10}^{-6}m=3.282\times {10}^3\stackrel{o}{A}$