Question

Gamma rays are photons with very high energy. How many visible-light photons with a wavelength of 500 nm would you need to match the energy of a gamma-ray photon with energy 2.1×10⁻¹³ J? (h = 6.626 × 10⁻³⁴ J · s, c = 3.00 × 10⁸ m/s)

Answer 1

There are needed 5.28*10⁵ photons.

Step-by-step explanation:

The energy of a photon of wavelength 500 nm can be calculated from the formula:

`E=(hc)/(\lambda)`

Where E is the energy of the photon, h is the Planck's constant and c is the speed of light in vacuum.

Next, since we are comparing this energy with the energy of a gamma-ray photon, we can say that this energy multiplied by the number of photons should be equal to the energy of gamma-ray photon:

`E_(\gamma)=nE_(light)=n((hc)/(\lambda))`

And solving for the number of photons, we get:

`n=\frac{E{\gamma}\lambda}{hc}\\ \\n=((2.1*10^(-13)J)(500*10^(-9)m))/((6.626*10^(-34)Js)(3.00*10^8m/s))\\\\n=5.28*10^5`

So, there are needed 5.28*10⁵ visible-light photons of wavelength 500nm to match the energy of a single gamma-ray photon with energy 2.1*10⁻¹³J.