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The Planck’s constant is $6.6 \times {10^{34}}Js$. The speed of light is $3 \times {10^{17}}nm{s^{ - 1}}$. Which value is closest to the wavelength in nanometers of a quantum of light with a frequency of $6 \times {10^{15}}{s^{ - 1}}$?
A. 10
B. 25
C. 50
D. 75

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Last updated date: 17th Jun 2024
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Answer
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Hint: The Planck’s constant is a natural constant named after Max Planck. Photon energy is the energy carried by a single photon. The amount of energy is directly proportional to the photon’s electromagnetic frequency and thus equivalently, is inversely proportional to the wavelength.

Formula used:
 $\lambda = \dfrac{c}{\nu }$ Where, c is the speed of light
v Is the frequency of quanta and $\lambda $ is the wavelength.

Complete step by step answer:
Wavelength is basically the distance between the identical points in the adjacent cycles of a waveform signal propagated in space or along a wire.
Now, let’s solve the given question. We have been given the value of Planck’s constant, the speed of light and the frequency of the quanta. We have to find its wavelength.
Now, Planck’s constant h $ = 6.63 \times {10^{ - 34}}Js$
Speed of light c $ = 3 \times {10^{17}}nm{s^{ - 1}}$
Frequency of quanta $\nu = 6 \times {10^{15}}{s^{ - 1}}$
We have to find $\lambda $
We know that,
$h = \dfrac{c}{\lambda }$
Or $\lambda = \dfrac{c}{\nu }$
Now, substitute the values,
$\lambda = \dfrac{{3 \times {{10}^{17}}nm{s^{ - 1}}}}{{6 \times {{10}^{15}}{s^{ - 1}}}}$
$\lambda = 50nm$

Hence, option C is correct.

Note:
All electromagnetic waves travel at the speed of light in a vacuum but they travel at slower speeds when they travel through a medium that is not a vacuum. Other waves such as sound waves travel at much lower speeds and cannot travel through a vacuum.