Question

The value of Planck's constant is $6.63\times {10}^{-34}J-s$. The velocity of light is $3\times {10}^{8}m/sec$. Which value is closest to the wavelength in nanometer of a quantum of light with frequency of $8\times {10}^{15}{sec}^{-1}$?

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

Answer 1

Answer: (B)

$4\times {10}^1$

The speed of light $C=3\times {10}^{8}m/sec$
The frequency $\nu =8\times {10}^{15}{sec}^{-1}$

$\lambda =\frac{C}{\nu }$

$\lambda =\frac{3\times {10}^{8}m/sec}{8\times {10}^{15}{sec}^{-1}}$
$\lambda =3.75\times {10}^{-8}m$

$\lambda =37.5\times {10}^{-9}m$

$\lambda \simeq 40nm\simeq 4\times {10}^{1}nm$

Hence, the correct option is $\text{B}$