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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 $6 \times 10^{15} \mathrm{~s}^{-1} ?$
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Verified Answer
The correct answer is:
50
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
$$
\begin{aligned}
\lambda & =\frac{c}{v} \\
& =\frac{3 \times 10^{17}}{6 \times 10^{15}} \\
& =0.5 \times 10^2 \mathrm{~nm} \\
& =50 \mathrm{~nm}
\end{aligned}
$$
$$
h=6.63 \times 10^{-34} \mathrm{~J}-\mathrm{s}
$$
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
$$
\begin{aligned}
\lambda & =\frac{c}{v} \\
& =\frac{3 \times 10^{17}}{6 \times 10^{15}} \\
& =0.5 \times 10^2 \mathrm{~nm} \\
& =50 \mathrm{~nm}
\end{aligned}
$$
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