Question

The maximum wavelength of radiation that can produce photoelectric effect in a certain metal is $2000\mathring{\text{A}}$. The maximum kinetic energy acquired by an electron due to radiation of wavelength $1000\mathring{\text{A}}$ will be nearly

• A. $3.4\text{eV}$
• B. $6.2\text{eV}$
• C. $1.2\text{eV}$
• D. $12.4\text{eV}$

Answer 1

The correct option is B $6.2\text{eV}$

From Einstein’s photoelectric equation,

$\frac{hc}{\lambda }=\frac{hc}{{\lambda }_0}+k_{max}$

Maximum kinetic energy of electron emitted,

$k_{max}=hc\left[\begin{array}{c}\frac{1}{\lambda }-\frac{1}{{\lambda }_0}\end{array}\right]\text{J}$

$\Rightarrow k_{max}=\frac{hc}{e}\left[\begin{array}{c}\frac{1}{\lambda }-\frac{1}{{\lambda }_0}\end{array}\right]\text{eV}$

$=12400\left[\begin{array}{c}\frac{1}{1000}-\frac{1}{2000}\end{array}\right]\text{eV}$

$=12400\times \frac{1}{2000}=6.2\text{eV}$