Calculate the energy in joules of microwave radiation of wavelength 12.7 centimeters.
(E = hν, h = 6.63 × 10-34 J.sec; speed of light = wavelength × ν, speed of light = 3.0 × 108 meters/sec.)
7.3*10-19
E= hc/wavelength
h (6.63x12^-34) x c (3.0x10^8) = 1.99x10^-25 / 0.127m = 1.6x10^-24
remembering you have to convert cm to m
Well, if I may interject with a funny observation before answering your question... Have you noticed that every time you heat up a burrito in the microwave, you always end up with one side scorching hot while the other side is still frozen? It's like the microwave has a personal vendetta against burritos! Anyway, let's get back to the energy calculation.
To find the energy in joules, we can use the formula E = hν, where h is the Planck's constant (6.63 × 10^(-34) J·s) and ν (nu) is the frequency.
Now, speed of light = wavelength × ν, and we can rearrange this formula to find the frequency: ν = speed of light / wavelength.
So, let's calculate the frequency first:
ν = 3.0 × 10^8 m/s / (12.7 cm) = (3.0 × 10^8 m/s) / (0.127 m) = 2.36 × 10^9 Hz.
Now, we can plug this frequency into the energy formula:
E = (6.63 × 10^(-34) J·s) × (2.36 × 10^9 Hz) = 1.56 × 10^(-24) J.
So, the energy of microwave radiation with a wavelength of 12.7 cm is approximately 1.56 × 10^(-24) joules. Now, that's quite a tiny amount of energy, ain't it? It's like the energy equivalent of losing a sock in the dryer. Blink, and it's gone!
To calculate the energy in joules of microwave radiation, we will use the formula E = hν, where E is the energy, h is Planck's constant, and ν is the frequency of the radiation.
First, we need to find the frequency of the microwave radiation using the equation: speed of light = wavelength × ν.
Given: speed of light = 3.0 × 10^8 meters/sec and wavelength = 12.7 centimeters.
To convert the wavelength from centimeters to meters, we need to divide by 100:
wavelength = 12.7 cm = 12.7 / 100 m = 0.127 m.
Now we can rearrange the speed of light equation to solve for frequency:
speed of light = wavelength × ν
ν = speed of light / wavelength
ν = 3.0 × 10^8 m/s / 0.127 m.
Calculating the frequency:
ν = 2.3622 × 10^9 Hz.
Now that we have the frequency, we can calculate the energy using the formula E = hν.
Given: h = 6.63 × 10^-34 J·sec and ν = 2.3622 × 10^9 Hz.
Calculating the energy:
E = (6.63 × 10^-34 J·sec) * (2.3622 × 10^9 Hz).
Evaluating the expression:
E ≈ 1.5643 × 10^-24 J.
Therefore, the energy of microwave radiation with a wavelength of 12.7 centimeters is approximately 1.5643 × 10^-24 J.