The value of Planck's constant is 6.63 × 10^ -34 Js . The velocity of light is 3.0 × 10^8 ~ms^ -1 . Which value is closest to the wavelength in nanometers of quantum of light with frequency of 8 × 10^ 15 ~s^ -1 ?

Correct answer: C. 4 × 10^1 aligned & c=v × λ ; λ=(c)/(v) & λ= 3 × 10^8 8 × 10^ 15 =0.375 × 10^ -7 ~m & =0.375 × 10^ -7 × 10^9 ~nm & =0.375 × 10^2 ~nm & =37.5 ~nm & 4 × 10 ~nm aligned

NEET 2003

Exam: NEET
Year: 2003
Subject: Chemistry
Chapter: Structure of Atom

NEET 2003 · Chemistry · Structure of Atom

The value of Planck's constant is 6.63 × 10^ -34 Js . The velocity...

The value of Planck's constant is 6.63

\times 10^{-34} \mathrm{Js}

. The velocity of light is

3.0 \times

10^8 \mathrm{~ms}^{-1}

. Which value is closest to the wavelength in nanometers of quantum of light with frequency of

8 \times 10^{15} \mathrm{~s}^{-1}

Options

A $2 \times 10^{-25}$
B $5 \times 10^{-18}$
C $4 \times 10^1$
D $3 \times 10^7$

Correct answer

C. $4 \times 10^1$

Step-by-step solution

\begin{aligned} & c=v \times \lambda ; \lambda=\frac{c}{v} \\ & \Rightarrow \lambda=\frac{3 \times 10^8}{8 \times 10^{15}}=0.375 \times 10^{-7} \mathrm{~m} \\ & =0.375 \times 10^{-7} \times 10^9 \mathrm{~nm} \\ & =0.375 \times 10^2 \mathrm{~nm} \\ & =37.5 \mathrm{~nm} \\ & \approx 4 \times 10 \mathrm{~nm} \end{aligned}

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