Question

U.V. light of wavelength 800 A & 700 A falls on hydrogen atoms in their ground state & liberates electrons with kinetic energy 1.8eV and 4eV respectively, the Planck's constant is:

• A. $6.57\times {10}^{-34}Js$
• B. $6.89\times {10}^{-34}Js$
• C. $7.34\times {10}^{-34}Js$
• D. $7.23\times {10}^{-34}Js$

Answer 1

Answer: (A)

$6.57\times {10}^{-34}Js$

$\frac{hc}{\lambda }=KE+WorkFunction$
$\frac{hc}{{\lambda }_1}=K{E}_1+WorkFunction\to 1$
$\frac{hc}{{\lambda }_2}=K{E}_2+WorkFunction\to 2$
$hc[\frac{1}{{\lambda }_2}-\frac{1}{{\lambda }_1}]=K{E}_2-K{E}_1$
$hc[\frac{1}{700}-\frac{1}{800}]=4-1.8$
$\frac{hc}{5600}=2.2$
$\Rightarrow hc=2.2\times 1.6\times {10}^{-19}\times 5600\times {10}^{-10}Jm$
$\Rightarrow h=\frac{2.2\times 1.6\times {10}^{-19}\times 5600\times {10}^{-10}Jm}{3\times {10}^{8}m{s}^{-1}}$
$\Rightarrow h=6.57\times {10}^{-34}Js$