The value of Planck's constant is $6.63 \times 10^{-34} \mathrm{Js}$. The speed of light is $3 \times…

The value of Planck's constant is $6.63 \times 10^{-34} \mathrm{Js}$. The speed of light is $3 \times 10^{17} \mathrm{nms}^{-1}$. Which value is closest to the wavelength in nanometer of a quantum of light with frequency of $6 \times 10^{15} \mathrm{~s}^{-1} ?$
  1. 10
  2. 25
  3. 50
  4. 75

Solution

Given, Planck's constant, $h=6.63 \times 10^{-34} \mathrm{~J}-\mathrm{s}$ Speed of light, $c=3 \times 10^{17} \mathrm{~nm} \mathrm{~s}^{-1}$ Frequency of quanta $v=6 \times 10^{15} \mathrm{~s}^{-1}$ Wavelength, $\lambda=$ ? We know that, $v=\frac{c}{\lambda}$ or $\begin{aligned} \lambda & =\frac{c}{v} \\ & =\frac{3 \times 10^{17}}{6 \times 10^{15}} \\ & =0.5 \times 10^2 \mathrm{~nm} \\ & =50 \mathrm{~nm} \end{aligned}$

Asked in: NEET 2013 (All India)

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