The values of Planck's constant is $6.63 \times 10^{-34} \mathrm{Js}$. The velocity of light is $3.0 \times…

The values of Planck's constant is $6.63 \times 10^{-34} \mathrm{Js}$. The velocity of light is $3.0 \times 10^{8} \mathrm{~m} \mathrm{~s}^{-1}$. Which value is closest to
the wavelength in nanometres of a quantum of light with frequency of $8 \times 10^{15} \mathrm{~s}^{-1}$ ?
  1. $5 \times 10^{-18}$
  2. $4 \times 10^{1}$
  3. $3 \times 10^{7}$
  4. $2 \times 10^{-25}$

Solution

$\quad \mathrm{E}=\mathrm{hv}=\frac{\mathrm{ch}}{\lambda} ;$ and $v=\frac{\mathrm{c}}{\lambda}$
$8 \times 10^{15}=\frac{3.0 \times 10^{8}}{\lambda}$
$\therefore \lambda=\frac{3.0 \times 10^{8}}{8 \times 10^{15}}=0.37 \times 10^{-7}=37.5 \times 10^{-9} \mathrm{~m}=4 \times 10^{1}$ .

Asked in: JEE-TOPICTESTS-CHEMISTRY

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