# Calculate the energy, in joules, of a photon of green light having a wavelength of 562nm?

Apr 6, 2015

$E = 3.54 \times {10}^{- 19} \text{J}$

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

$E = \frac{6.626 \times {10}^{- 34} \times 3.00 \times {10}^{8}}{562 \times {10}^{- 9}} \text{J}$

$E = 3.537 \times {10}^{- 19} \text{J}$

Apr 6, 2015

The answer is $3.54 \times \text{10"^(-19)" J}$.

The equation for determining the energy of a photon of electromagnetic radiation is $E = h \nu$, where E is energy in Joules, h is Planck's constant, $6.626 \times \text{10"^(-34)"J"*"s}$, and $\nu$ (pronounced "noo") is the frequency.

You have been given the wavelength $\lambda$ (pronounced lambda) in nanometers, but not the frequency.

Fortunately, a relationship between wavelength, frequency, and the speed of light, $c$ exists, such that $c = \lambda \cdot \nu$. To determine the frequency from the wavelength, divide $c$ by $\lambda$:

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

We can substitute $\frac{c}{\lambda}$ for $\nu$ in the first equation, so that:

$E = h \cdot \frac{c}{\lambda}$

The speed of light, $c$, is usually given as $3.00 \times {10}^{8} \text{m/s}$ rounded to three significant figures. So the wavelength must first be converted from nm to m. $1 \text{m"=1xx10^9 "nm}$. To convert nm to m, do the following calculation:

562 color(red)cancel(color(black)( "nm"))xx(1"m")/(1xx10^9 color(red)cancel(color(black)("nm")))="0.000000562m"=5.62xx"10"^(-7) "m"

Now we're ready to determine the amount of energy in Joules in one photon of green light with the wavelength $\text{562 nm}$.

$E = h \nu = h \cdot \frac{c}{\lambda}$

Substitute the known values into the equation and solve.

$6.626 \times \text{10"^(-34)"J"*color(red)cancel(color(black)("s"))xx(3.00xx"10"^8color(red)cancel(color(black)("m"))/color(red)cancel(color(black)("s")))/(5.62xx"10"^(-7)color(red)cancel(color(black)("m")))=3.54xx"10"^(-19)" J}$