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.

You have all of the formulas and the numbers there, what's the problem? By the way, you must change 12.7 cm to m. Also, you don't have wavelenth in the formula; I would use E = hc/wavelength.