Each photon in a beam of light has an energy of $4.20 \mathrm { eV }$. What is the wavelength of this light? $( c =$ $3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J}$ )
A) $296 \mathrm {~nm}$
B) $420 \mathrm {~nm}$
C) $103 \mathrm {~nm}$
D) $412 \mathrm {~nm}$
E) $321 \mathrm {~nm}$

Question

Quizplus · Accepted Answer

The energy of a photon is given by $E = hf$, where $h$ is Planck's constant and $f$ is the frequency of the light. The wavelength of light is given by $\lambda = c/f$, where $c$ is the speed of light. Substituting the given values into these equations, we get:$$E = hf = (6.626 \times 10^{-34} \mathrm{J} \cdot \mathrm{s})(4.20 \mathrm{eV})(1.60 \times 10^{-19} \mathrm{J/eV}) = 4.41 \times 10^{-19} \mathrm{J}$$$$\lambda = c/f = (3.00 \times 10^8 \mathrm{m/s})/(4.41 \times 10^{14} \mathrm{Hz}) = 296 \mathrm{nm}$$Therefore, the wavelength of the light is 296 nm.

Each Photon in a Beam of Light Has an Energy 4.20eV4.20 \mathrm { eV }4.20eV

Each Photon in a Beam of Light Has an Energy $4.20 \mathrm { eV }$