Question

What wavelength of radiation has photons of energy 2.87×x10−18 j?

Answer 1

The energy of a photon is given by
$E=hf$
where h is the Planck constant and f is the frequency of the light. 
Given the relationship between the frequency f, the wavelength $\lambda$ and the speed of light c for an electromagnetic wave:
$f= \frac{c}{\lambda}$
we can rewrite the energy of the photon as
$\lambda = \frac{hc}{E}$
and by substituting $h=6.6 \cdot 10^{-34 J}$, $c=3 \cdot 10^8 m/s$ and $E=2.87 \cdot 10^{-18}J$, we get the wavelength of the photon:
$\lambda = \frac{hc}{E}=6.9 \cdot 10^{-8} m = 69 nm$