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cryssatemp

Answer: [tex]E=4.321(10)^{-19} J[/tex]

Explanation:

The energy [tex]E[/tex] of a photon is given by:

[tex]E=h\nu[/tex] (1)

Where:

[tex]h=6.626(10)^{-34}\frac{m^{2}kg}{s}[/tex] is the Planck constant

[tex]\nu[/tex] is the frequency light

On the other hand, there is an inverse relationship between [tex]\nu[/tex]  and the wavelength [tex]\lambda[/tex]:

[tex]\nu=\frac{c}{\lambda}[/tex] (2)

Where:

[tex]c=3(10)^{8} m/s[/tex] is the speed of light

[tex]\lambda=460 nm=460(10)^{-9}m[/tex] is the wavelength

Substituting (2) in (1):

[tex]E=\frac{hc}{\lambda}[/tex] (3)

[tex]E=\frac{(6.626(10)^{-34}\frac{m^{2}kg}{s})(3(10)^{8} m/s)}{460(10)^{-9}m}[/tex]

Finally:

[tex]E=4.321(10)^{-19} J[/tex] This is the energy of a photon of blue light, in Joules.

facundo3141592

We want to find the energy of a photon given that we know its wavelength.

We will see that the energy of the photon is:

[tex]E = 4.3*10^{-9} J[/tex]

Now let's see how to get the answer:

The energy of a photon of wavelength λ is given by:

[tex]E =\frac{h*c}{ \lambda}[/tex]

Where:

[tex]h = 6.626*10^{-34} J\cdot s[/tex]

[tex]c = 3*10^8 m/s[/tex]

So we need to rewrite our wavelength in meters instead of nanometers, so the units coincide.

we know that:

[tex]1 nm = 1*10^{-9} m[/tex]

Then:

[tex]460 nm = 460*10^{-9} m = 4.6*10^{-7} m[/tex]

Now that we know all the values we need to use in the energy equation, we can write:

[tex]E = \frac{(3*10^8m/s)*(6.626*10^{-34} J*s}{4.6*10^{-7}} = 4.3*10^{-9} J[/tex]

So we just found the energy of the photon.

If you want to learn more, you can read:

https://brainly.com/question/23180082