Question

Light of wavelength ${\lambda }_A$ and ${\lambda }_B$ falls on two identical metal plates $A$ and $B$ respectively. The maximum kinetic energy of photoelectrons in $K_A$ and $K_B$ respectively, then which one of the following relations is true? $({\lambda }_A=2{\lambda }_B)$

• A. $K_A<\frac{K_B}{2}$
• B. $2K_A=K_B$
• C. $K_A=2K_B$
• D. $K_A>2K_B$

Answer 1

The correct option is A $K_A<\frac{K_B}{2}$

According to Einstein photoelectric equation
$K_A=\frac{hc}{{\lambda }_A}-\varphi \Rightarrow 2K_A=\frac{2hc}{{\lambda }_A}-2\varphi$
or $2K_A+\varphi =\frac{2hc}{{\lambda }_A}-\varphi$
Wavelength of metal $B$ is half of metal $A$
$\therefore 2K_A+\varphi =K_B$
$\Rightarrow K_A<\frac{K_B}{2}$