Question

An electron moving with speed v₁ has wavelength $\lambda_{1}$ and another electron moving with speed v₂ has wavelength $\lambda_{2}$, find (v₁² - v₂²). (m_e = mass of electron)

• A. $\frac{2h}{m_{e}}\left(\frac{1}{\lambda_{2}}-\frac{1}{\lambda_{1}}\right)^{2}$
• B. $\frac{2h}{m_{e}}\left(\frac{1}{\lambda_{2}}-\frac{1}{\lambda_{1}}\right)$
• C. $\frac{h^{2}}{m_{e}}\left(\frac{1}{\lambda_{2}}-\frac{1}{\lambda_{1}}\right)$
• D. $\frac{h^{2}}{2m_{e}}\left(\frac{1}{\lambda^{2}_{1}}-\frac{1}{\lambda_{2}^{2}}\right)$

Answer 1

Answer: (D)

$v^{2}_{1}-v^{2}_{2}=\frac{p^{2}_{1}}{2m_{e}}-\frac{p^{2}_{2}}{2m_{e}}=\frac{h^{2}}{2m_{e}}\left(\frac{1}{\lambda^{2}_{1}}-\frac{1}{\lambda^{2}_{2}}\right)$