Solution of the schrödinger wave equation for the hydrogen atom results in a set of functions (orbitals) that describe the behavior of the electron. each function is characterized by 3 quantum numbers: n, l, and ml. if the value of n = 1 the quantum number l can have values from to . the total number of orbitals possible at the n = 1 energy level is . if the value of l = 1 the quantum number ml can have values from to . the total number of orbitals possible at the l = 1 sublevel is .

If n=1, l can only have the value l=0 and the total number of orbitals is 0. If l=1, ml can be -1,0 or 1 and the total number of orbitals at l=1 is 3.

Explanation:

When solving the radial part of Schrödinger equation, one needs to expand in power series that lead to Laguerre polynomials of the form , being n and l the quantum numbers. As is known, in the Laguerre polynomials the subindex must be greater than or equal to 0, which implies . So if n=1, the only possible value of l is l=0.

Likewise, when solving the angular part, one gets the spherical harmonics can be . Therefore the sublevel l=| has 3 possible orbitals.

answer : one can design an experiment using a liquid and an additive that can be added to the liquid and observe the chemical changes in the reaction species.

one would need a beaker which is filled with a known amount of the liquid in which thermometer is placed to measure the temperature changes; after addition of the additive to the liquid solution one can note down the temperature change and find whether the reaction is endothermic or exothermic in nature. by subtracting the initial temperature value with the final temperature one can find the temperature changes.

various combinations of liquid and additive can be used. liquid in this case can be a known quantity of water and additives can be epsom salt or without epsom salt the experiment can be conducted to notice the changes. water and ice, hydrogen peroxide and dry yeast, vinegar and baking soda,etc.