Question

The values 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 nanometres of a quantum of light which frequency of $8\times {10}^{15}{s}^{-1}$?

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

Answer 1

The correct option is B $4\times {10}^1$

For light, the energy E is given by $E=hf$ and also by $E=hc/\lambda$, where h is Planck's constant, f is the frequency, c is the speed of light, and $\lambda$ is the wavelength. So, we have:

$hf=\frac{hc}{\lambda }$

$f=\frac{c}{\lambda }$

$f\lambda =c$

$\lambda =\frac{c}{f}$

$\lambda =(3.0\times {10}^8)/(8\times {10}^{15})$

$\lambda =3.75\times {10}^{-8}$ m

$\lambda =4\times {10}^1$ nm