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Green light has a frequency of about 6.00 x 10^14 s-1 . What is the energy...

Green light has a frequency of about 6.00 x 10^14 s-1 . What is the energy of a photon of green light?
4 sigfig
E=J

If you have time can you answer this one too??

Hospital X-ray generators emit X rays with wavelength of about 15.0 nanometers (), where 1 nm = 10^9 m. What is the energy of a photon in an X ray?
Express answer in joules.

And please show me all the details on how you arrived to your answers. Thank you very much!
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Homework Answers

Answer #1
Concepts and reason

The concept used to solve this problem is based on the energy of a photon.

The energy of the photons is calculated using the Planck’s law when their frequency is known. The energy can also be calculated when only the wavelength is known. The wave equation is used to first calculate the frequency and then it is substituted in the Planck’s equation.

Fundamentals

The energy of a photon can be calculated using the Planck’s equation:

E hu

Here, Е is the energy of photons , h is the Planck’s constant ( s) .626 *10J S and is the frequency of the photon (s) .

The relationship between the speed of the light, frequency and wavelength is provided by the wave equation:

c Av

Here, is the speed of light 3x10 m s , is the wavelength of the photon and is the frequency.

Part 1

It is known that the frequency (v) of the green light is6.00x1014 s .-1 S .

According to Planck’s equation,

E hu

Substitute 6.00x101s for and 6.626x10 34JS for Planck’s constanth .

E 6.626x103J sx6.00x1014 s1 39.756x102J -3.9756x1019 J 3.976x1019 J

Part 2

It is known that the wavelength of the X-ray is 15.0 nm .

a 15.0 nm

Since,

1 nm 10 m

Therefore,

15.0 nm 15.0x 10 m

According to Planck’s equation,

E hu

According to wave equation,

c Av

The equation can be rewritten as:

C v=

Substitute this expression of frequency in the Planck’s equation.

E hu c E=h

Substitute |6.626x1034 J s for Planck’s constant , 3x108 ms for and 15.0x10 m for in the above expression.

(6.626x10J s)x3x10 ms 15.0x10 m E = 1.325x1017 J

Ans: Part 1

Part 1

Answer

The energy of a photon of green light is 3.976x1019 J .

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