To solve this problem we will use the concept related to electrons in a box which determines the energy of an electron in that state.
Mathematically this expression is given by,
![E_n= \frac{n^2h^2}{8mL^2}](https://tex.z-dn.net/?f=E_n%3D%20%5Cfrac%7Bn%5E2h%5E2%7D%7B8mL%5E2%7D)
Where,
m = mass of an electron
h = Planck's constant
n = is the integer number of the eigenstate
L = Quantum well width
The change in energy must be given in state 1 and 2, therefore
![\Delta E = E_2 - E_1](https://tex.z-dn.net/?f=%5CDelta%20E%20%3D%20E_2%20-%20E_1)
![\Delta E = \frac{2^2h^2}{8mL^2}-\frac{1^2h^2}{8mL^2}](https://tex.z-dn.net/?f=%5CDelta%20E%20%3D%20%5Cfrac%7B2%5E2h%5E2%7D%7B8mL%5E2%7D-%5Cfrac%7B1%5E2h%5E2%7D%7B8mL%5E2%7D)
![\Delta E = \frac{3h^2}{8mL^2}](https://tex.z-dn.net/?f=%5CDelta%20E%20%3D%20%5Cfrac%7B3h%5E2%7D%7B8mL%5E2%7D)
Replacing we have:
![(4*1.6*10^{-19}) = \frac{3(6.626*10^{34})}{8*(9.11*10^{-31})*L^2}](https://tex.z-dn.net/?f=%284%2A1.6%2A10%5E%7B-19%7D%29%20%3D%20%5Cfrac%7B3%286.626%2A10%5E%7B34%7D%29%7D%7B8%2A%289.11%2A10%5E%7B-31%7D%29%2AL%5E2%7D)
![L = 0.53nm](https://tex.z-dn.net/?f=L%20%3D%200.53nm)
Therefore the correct answer is C.
Because when you open the faucet, you want the water to
rush out with pressure, not just dribble or ooze out. The
water has to be supplied to the user with pressure. Either
you supply it from a height, or else you'll need to use pumps
to make the pressure.
Answer:
The independent variable is the number of dry cells and the dependent variable is the time the bulb works.
Explanation:
In this exercise, you are asked to analyze the variables derived from Ómar's hypotypeis
"If more dry cells are connected end-to-end, a light bulb will work longer because more energy is available."
In this hypothesis, the independent variable that is controlled by the researcher is the number of batteries to be connected in series.
The dependent variable that is measured by the researcher is how long the bulbs last.
When reviewing the different answers, the correct one is:
The independent variable is the number of dry cells and the dependent variable is the time the bulb works.