Question

Two particles $A_{1}$and $A_{2}$of masses $m_{1,}m_{2}$ ($m_{1} > m_{2}$) have the same de Broglie wavelength. Then

• A. Their momenta are the same.
• B. Their energies are the same.
• C. Momentum of $A_{1}$is less than the momentum of $A_{2}$
• D. Energy of $A_{1}$is more than the energy of $A_{2}$

Answer 1

Answer: (A)

Their momenta are the same.

Answer 2

: As$\lambda = \frac{h}{p}orp = \frac{h}{\lambda}orp \propto \frac{1}{\lambda}$

$\therefore\frac{p_{1}}{p_{2}} = \frac{\lambda_{2}}{\lambda_{1}} = \frac{\lambda_{}}{\lambda_{}} = 1orp_{1} = p_{2}$

Also $E = \frac{1}{2}\frac{p^{2}}{m} = \frac{1}{2m}\frac{h^{2}}{\lambda^{2}}$ $\left( \therefore p = \frac{h}{\lambda} \right)$

Or $E \propto \frac{1}{m}\therefore\frac{E_{1}}{E_{2}} = \frac{m_{2}}{m_{1}} < 1orE_{1} < E_{2}$