Question

The value of Planck's constant is $ 6.63\times {{10}^{-34}} $ Js. The velocity of light is $ 3.0\times {{10}^{8}}m{{s}^{-1}} $ . Which value is closest to the wavelength (in nm) of a quantum of light with frequency of $ 8\times {{10}^{-1}}{{s}^{-1}} $ ?

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

Answer 1

Answer: (A)

$ \Rightarrow $ $ Frequency=\frac{velocity\text{ }of\text{ }light\text{ }(c)}{wavelength\,(\lambda )} $ Given, frequency
$=8\times {{10}^{15}}{{s}^{-1}} $ velocity of light
$=3.0\times {{10}^{8}}m{{s}^{-1}} $
$ \therefore $ $ 8\times {{10}^{15}}=\frac{3\times {{10}^{8}}}{\lambda } $ or $ \lambda =\frac{3\times {{10}^{8}}}{8\times {{10}^{15}}}=0.375\times {{10}^{-7}}m $
$=3.75\times {{10}^{1}}nm $ $ \approx 40\,nm $