Hi there, I need help on my homework for chemistry and I do not understand the step on how to work this problem out. Please help me with this problem:
On a Sunday morning while having your breakfast you determine that you need about 2.95X10^(5)J to heat water for your tea in the microwave. If 2.5X10^(24) photons hit the cup every second and you set the timer to 2.4 min, what should the frequency of the microwave be so that the tea is ready in that time?
•Convert the minutes to seconds.
•Multiply (photons/sec) by number of seconds to get the total number of photons.
•Divide total joules by numer of photons to get the energy of a photon.
• E(photon) = h*f (f = freq.)
Substitute E and h into the above formula and solve for f.
2.4 min x (60s/1min) x 2.5 x 10^24 photons/s = 3.6 x 10^26 photons
energy per photon = 2.95 x 10^5 J/3.6 x 10^26 photon = 8.2 x 10^-22 J/photon
Now, E = hf
f = E/h
f = 8.2 x 10^-22 J/6.626 x 10^-34 J.s
f = 1.2 x 10^12 s^-1
To solve this problem, you need to understand the relationship between energy, frequency, and the number of photons.
First, let's break down the problem:
1. You need to find the frequency of the microwave to heat the water for a specific time.
To find the frequency, we can use the equation:
E = h * f
Where:
E = energy (in joules)
h = Planck's constant (6.626 x 10^(-34) J*s)
f = frequency (in Hz)
In this problem, the energy required to heat the water is given as 2.95 x 10^(5) J.
The number of photons hitting the cup every second is given as 2.5 x 10^(24).
Since energy of a photon can be calculated using the equation:
E(photon) = h * f(photon)
We can find the energy for each photon based on the given values.
Next, let's calculate the energy of one photon:
E(photon) = E / N
Where:
E(photon) = energy of one photon (in J)
E = energy required to heat the water (in J)
N = number of photons hitting the cup per second
Now, substitute the given values:
E(photon) = (2.95 x 10^(5) J) / (2.5 x 10^(24) photons/s)
Calculate this to find the energy of one photon.
Once you find the energy of one photon, you can rearrange the equation E(photon) = h * f(photon) to solve for the frequency.
f(photon) = E(photon) / h
Substitute the energy of one photon and Planck's constant into the equation and calculate the frequency.
Finally, since the problem asks for the frequency of the microwave, you can consider microwave radiation as electromagnetic radiation with the wavelength range of 0.3 to 30 cm. Using the speed of light (3.0 x 10^(8) m/s), you can calculate the frequency for microwave radiation.
I hope this explanation helps you understand how to solve this problem!