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. $\frac{h^2}{2m_e}\left(\frac{1}{{\lambda }_1^2}-\frac{1}{{\lambda }_2^2}\right)$

Answer 1

Answer: (D)

$v_1^2-v_2^2=\frac{p_1^2}{2m_e}-\frac{p_2^2}{2m_e}=\frac{h^2}{2m_e}\left(\frac{1}{{\lambda }_1^2}-\frac{1}{{\lambda }_2^2}\right)$