If you used only photons that were dropping from the n = 6 shell to the n = 1, how many of these photons would be required to keep a 100 Watt light bulb lit for 10 minutes?
You don't have enough information to answer this. I assume you are talking about the electron in a H atom. It will different for other elements.
How much energy do you get from a photon falling from n = 6 to n = 1? That's delta E = 2.180E-18J(1/1^2 - 1/6^2) = ?J/photon that you have.
How much energy is required to light a 100 watt bulb for 10 minutes?
100 watts = 100 J/s and for 10 minutes is 100 J/s x 10 min x (60 s/min)= ?J needed.
?J/photon x #photons = ?J needed.
Solve for # photons.
To determine the number of photons required to keep a 100 Watt light bulb lit for 10 minutes, we need to consider two concepts: the energy of each photon and the power (energy per unit time) of the light bulb.
First, let's determine the energy of a photon using the energy equation for the hydrogen atom:
E = -13.6 eV * (1/n_f^2 - 1/n_i^2),
where E is the energy of the photon, n_f is the final energy level (n = 1), and n_i is the initial energy level (n = 6).
Plugging in the values, we get:
E = -13.6 eV * (1/1^2 - 1/6^2) = 10.2 eV.
Next, we need to convert the energy from electron volts (eV) to joules (J) since power units are generally given in watts (J/s). Using the conversion factor of 1 eV = 1.6 x 10^-19 J, we find the energy of a photon in joules:
E = 10.2 eV * 1.6 x 10^-19 J/eV = 1.632 x 10^-18 J.
Now, let's calculate the energy consumed by a 100 Watt light bulb in 10 minutes:
Energy consumed = Power * Time = 100 W * 10 minutes * 60 seconds/minute = 6 x 10^4 J.
To find the number of photons required, we divide the total energy consumed by the energy of each photon:
Number of photons = Energy consumed / Energy per photon.
Substituting the values, we have:
Number of photons = (6 x 10^4 J) / (1.632 x 10^-18 J).
Evaluating this expression, we find that approximately 3.68 x 10^22 photons would be required to keep the 100 Watt light bulb lit for 10 minutes using only photons dropping from the n = 6 to n = 1 shell.