Final answer:
To heat the coffee, we need to calculate the energy of the coffee using Q = mcΔT. Then we calculate the energy of a single microwave photon using E = hf. Finally, we calculate the number of photons required using N = Q / E. The correct answer is d) 0.0042.
Step-by-step explanation:
To calculate the number of photons required to heat the coffee, we need to use the equation Q = mcΔT, where Q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
The heat required to heat the coffee can be calculated as Q = (200g) * (4.18J/g·°C) * (61°C - 25°C).
Next, we need to calculate the energy of a single microwave photon using the equation E = hf, where E is the energy, h is Planck's constant (6.63 x 10^-34 J·s), and f is the frequency.
Finally, we can calculate the number of photons required using the equation N = Q / E.
Plugging in the values, we get: N = (200g) * (4.18J/g·°C) * (61°C - 25°C) / (6.63 x 10^-34 J·s * 3 x 10^8 s^-1).
Simplifying the equation gives us: N ≈ 8.28 x 10^28 photons.
Therefore, the correct option is d) 0.0042.