When a photon of wavelength ${\lambda _1}$ is incident on a metal surface,the speed of the ejected fastest electron is $v_1 \ m/s$. If a photon of wavelength ${\lambda _2}$ is incident on the same metal,the speed of the ejected fastest electron is $v_2 \ m/s$. The value of $v_2^2 - v_1^2$ will be

• A
  $\frac{{2hc}}{{{m_e}}}\left[ {{\lambda _2} - {\lambda _1}} \right]$
• B
  $\frac{{2hc}}{{{m_e}}}{\left[ {{\lambda _2} - {\lambda _1}} \right]^2}$
• C
  $\frac{{2hc}}{{{m_e}}}\left[ {\frac{1}{{{\lambda _2}}} - \frac{1}{{{\lambda _1}}}} \right]$
• D
  $\frac{{2hc}}{{{m_e}}}{\left[ {\frac{1}{{{\lambda _2}}} - \frac{1}{{{\lambda _1}}}} \right]^2}$