GSM networks use microwaves of 20 cm in wavelength.
What is the energy carried by one trillion (10^12) photons of this wavelength is?
I got 10^-13 J, but this is apparently wrong. Please help!
energy of 1 photon
= (Plank constant x speed of light, c) / wavelength
= 6.626 x 10^-34 x 2.998 x 10^8 / 2 x 10^-1
= 9.93 x 10^-25 J
energy of 10^12 photons = 9.93 x 10^-25 x 10^12
= 9.93 x 10^-13 J
This was the answer I got too, but it was wrong. The options are:
a) 10^-16
b) 10^-15
c) 10^-14
d) 10^-13
e) 10^-12
To find the energy carried by one trillion photons of a particular wavelength, we need to use the equation E = hf, where E is the energy, h is Planck's constant (6.626 x 10^-34 J·s), and f is the frequency of the electromagnetic radiation.
To convert between wavelength (λ) and frequency (f) in the electromagnetic spectrum, we use the equation c = λf, where c is the speed of light (3 x 10^8 m/s).
First, we need to find the frequency corresponding to a wavelength of 20 cm:
λ = 20 cm = 0.2 m (since 1 cm = 0.01 m)
Using the equation c = λf, we can rearrange it to solve for f:
f = c / λ = (3 x 10^8 m/s) / (0.2 m) = 1.5 x 10^9 Hz
Now that we know the frequency, we can calculate the energy carried by one photon using the equation E = hf:
E = (6.626 x 10^-34 J·s) * (1.5 x 10^9 Hz) = 9.939 x 10^-25 J
Now, to find the energy carried by one trillion (10^12) photons, we simply multiply the energy per photon by the number of photons:
Energy = (9.939 x 10^-25 J) * (10^12) = 9.939 x 10^(-25 + 12) J = 9.939 x 10^-13 J
Based on these calculations, it seems that your initial answer of 10^-13 J is correct. It might be worth double-checking the calculations or making sure that the given values are accurate.