Question

At 200${}^o$C, hydrogen molecules have velocity 2.4 $\times$ 10${}^5$ cm s${}^{-1}$. The de Broglie wavelength in this case is approximately :

• A. 1 A${}^o$
• B. 1000 A${}^o$
• C. 100 A${}^o$
• D. 10 A${}^o$

Answer 1

The correct option is A 1 A${}^o$

$\lambda$ = $\frac{h}{mv}$ = $\frac{6.6\times {10}^{-27}ergs}{2/N_a\times 2.4\times {10}^{5}cm{s}^{-1}}$

(mass of 1 molecule of H${}_2$ = $\frac{2}{6.02\times {10}^{23}}$

= $\frac{6.6\times {10}^{-27}\times 6.02\times {10}^{23}}{2\times 2.4\times {10}^5}$

= 8.27 $\times$ 10${}^{-9}$ cm

= 0.8 $\times$ 10${}^{-8}$ cm = $0.8A^0$ = $1A^0$