1. Tardigrade
  2. Question
  3. Chemistry
  4. The threshold frequency of a metal corresponds to the wavelength of x nm. In two separate experiments ‘A’ and ‘B' incident radiations of wavelengths (1/2) x nm and (1/4) x nm respectively are used. The ratio of kinetic energy of the released electrons in experiment 'B' to that in experiment 'A' is

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Q. The threshold frequency of a metal corresponds to the wavelength of $x\, nm$. In two separate experiments ‘A’ and ‘B' incident radiations of wavelengths $\frac{1}{2} x \; nm$ and $\frac{1}{4} x \; nm $ respectively are used. The ratio of kinetic energy of the released electrons in experiment $'B'$ to that in experiment $'A'$ is

KEAMKEAM 2015Structure of Atom

Solution:

In experiment $A$, incident radiations of wavelength used $=\frac{1}{2} x$

In experiment $B$, incident radiations of wavelength used $=\frac{1}{4} x$

The ratio of kinetic energy of the released electrons in experiment ' $B$ ' to that in experiment ' A':

$\frac{( KE )_{B}}{( KE )_{A}}=\frac{\frac{1}{\lambda_{B}}-\frac{1}{\lambda_{0}}}{\frac{1}{\lambda_{A}}-\frac{1}{\lambda_{0}}}$ [lets $\lambda_{0}=x$]

$\frac{( KE )_{B}}{( KE )_{A}}=\frac{\frac{4}{x}-\frac{1}{x}}{\frac{2}{X}-\frac{1}{X}}=3$