Question

someone pls help thanks - Calculate the total energy in the 1.5x10^13 photons of gamma radiation having wavelength of 3.0x10^-12

Answer 1

Answer:

• 0.99 J

Explanation:

Photons are quanta of light (electromagnetic radiation).

The energy of a photon can be determined using the Planck-Einstein's equation:

• E = hυ = h×c/λ

Where:

• E is the energy of one photon

• h is Planck's constant = 6.626 × 10 ⁻³⁴ J.s

• υ is the frequency

• c is the speed of light, which you can approximate to 3.00×10⁸ m/s

• λ is the wavelength (3.0 × 10⁻¹² m for this problem)

Substituting the data in the equation, you get:

• E =  6.626 × 10 ⁻³⁴ J.s × 3.00×10⁸ m/s / 3.0 × 10⁻¹² m = 6.626×10⁻¹⁴ J

Since that is the energy of one photon, multiply by the number of photons to get the total energy:

• Total energy =  6.626×10⁻¹⁴ J/ photon × 1.5 × 10¹³ photon = 0.99 J

Answer: 0.99 J (rounded to two significant figures).

Answer 2

Answer:

Total energy is 9.932 × 10^-1 Joules

Explanation:

Using the concept on energy of photons

Energy of a photon, E, is given by;

E = hf, where h is the plank's constant and f is the frequency of the radiation.

But, since frequency is given by dividing the velocity, c, by wavelength, λ,

Then; E = hc/λ

In this case; we are given more than one photons.

Therefore;

Energy = n × hc/λ , where n is the number of photons

Given;

n (the number of photons) = 1.5x10^13 photons

h (plank's constant) = 6.626× 10^-34 J/s

c (speed of light in vacuum) = 2.998 x 10^8 m/s

λ (wavelength of the radiation) = 3.0x10^-12 m

We can calculate energy;

     Energy =  (nhc)/λ ,

$Energy = \frac{(1.5.10^{13})(6.626.10^{-34} J/s)(2.998.10^8 m/s)}{3.0.10^{-12} m}$

                  = 9.932 × 10^-1 Joules

Thus the total energy in the 1.5x10^13 photons is 9.932 × 10^-1 Joules