Looking for classes? Ksquare Career Institute, Bengaluru →
The value of Planck's constant is $6.63 \times 10^{-34}$ J s. The velocity of light is $3.0 \times 10^8$ m s$^{-1}$. Which value is closest to the wavelength in nanometers of a quantum of light with frequency of $8 \times 10^{15}$ s$^{-1}$ :
A
$2 \times 10^{-25}$
B
$5 \times 10^{-18}$
C
$4 \times 10^{1}$
D
$3 \times 10^{7}$
Detailed Solution
Wavelength and frequency are related by $c = \nu\lambda$ (Planck's constant is not needed).
$\lambda = \dfrac{c}{\nu} = \dfrac{3.0 \times 10^8}{8 \times 10^{15}} = 3.75 \times 10^{-8}$ m
1 nm $= 10^{-9}$ m, so $\lambda = 3.75 \times 10^{-8} \times 10^{9} = 37.5$ nm
The closest value is $4 \times 10^1$ nm.
$\lambda = \dfrac{c}{\nu} = \dfrac{3.0 \times 10^8}{8 \times 10^{15}} = 3.75 \times 10^{-8}$ m
1 nm $= 10^{-9}$ m, so $\lambda = 3.75 \times 10^{-8} \times 10^{9} = 37.5$ nm
The closest value is $4 \times 10^1$ nm.