Question

A radio antenna radiates 3.47 W of power at 185 Hz.

How many photons per second are emit-
ted by the antenna? Planck's constant is
6.63 x 10-34 J·s.

Answer 1

To calculate the number of photons emitted per second by a radio antenna, you need to use Planck's constant to find the energy per photon based on the frequency and then divide the total power output by the energy per photon.

Step-by-step explanation:

The question asks to calculate how many photons per second are emitted by a radio antenna radiating power at a specific frequency. The pertinent formula involved is the calculation of the energy of a photon using Planck's constant and the frequency of the radiation, and then determining how many such photons are emitted per second given the total power output. This requires knowledge of the relationship between energy, power, and photons, as well as the ability to perform unit conversions where necessary.

To find the number of photons emitted per second by the antenna, we can use the formula:

E = hν

where E is the energy per photon, h is Planck's constant (6.63 x 10^-34 J·s), and ν (nu) is the frequency of the radiation. Then, the number of photons emitted per second (N) is the total power (P) divided by the energy per photon (E):

N = P / E

For example, if the antenna radiates 3.47 W of power at 185 Hz, the energy per photon is:

E = (6.63 x 10^-34 J·s)(185 Hz) = 1.22655 x 10^-31 J

Then, the number of photons per second is:

N = 3.47 W / 1.22655 x 10^-31 J/photon.

Answer 2

"
`2.829* 10^(31) \ photon/s`" is the appropriate solution.

Step-by-step explanation:

The given values are:

Power,

P = 3.47 W

Frequency,

f = 185 Hz

Planck's constant,

h = 6.63 x 10⁻³⁴ J.s

As we know,

⇒
`n=(P)/(E)`

Or,

⇒
`n=(P)/(hf)`

On substituting the given values, we get

⇒
`=(3.47)/(6.63* 10^(-34)* 185)`

⇒
`=(3.47)/(1.22655* 10^(-31))`

⇒
`=2.829* 10^(31) \ photon/s`