Question

what is the energy (in eV units) carried by one photon violet light that has a wavelength of 4.5e-7?

Answer 1

The energy of a photon is given by
$E=hf$
where h is the Planck constant and f is the photon frequency.

We can find the photon's frequency by using the following relationship:
$f= \frac{c}{\lambda}$
where c is the speed of light and $\lambda$ is the photon's wavelength. By plugging numbers into the equation, we find
$f= \frac{c}{\lambda}= \frac{3 \cdot 10^8 m/s}{4.5 \cdot 10^{-7} m}=6.67 \cdot 10^{14}Hz$

And so now we can find the photon energy
$E=hf=(6.6 \cdot 10^{-34} Js)(6.67 \cdot 10^{14}Hz )=4.4 \cdot 10^{-19} J$

We know that 1 Joule corresponds to
$1 J = 1.6 \cdot 10^{-19} eV$
So we can convert the photon's energy into electronvolts:
$E= \frac{4.4 \cdot 10^{-19} J }{1.6 \cdot 10^{-19} J/eV}=2.75 eV$