A certain shell is known to have a total of 16 orbitals, which shell is it?
Wouldn't that be n = 4?
Why? How do we know that it is n=4?
n^2=16
n^2=4^2
n^2=4
sorry...
n=4
To determine the shell with a total of 16 orbitals, we first need to understand the orbital filling order in an atom. The order is given by the Aufbau principle, which states that electrons fill orbitals in order of increasing energy.
According to the Aufbau principle, orbitals are grouped into different energy levels or shells. The shells are labeled by integers: 1, 2, 3, and so on, with the first shell being the lowest in energy.
Each shell consists of subshells, which are further divided into orbitals. Subshells are labeled by a combination of a shell number and a letter: s, p, d, f. For example, the subshells in the second shell are labeled as 2s and 2p.
The total number of orbitals in a shell can be found by using the formula 2n^2, where n represents the shell number. For example, the first shell (n = 1) has 2(1)^2 = 2 orbitals, and the second shell (n = 2) has 2(2)^2 = 8 orbitals.
To find the shell with a total of 16 orbitals, we can use the formula and solve for n:
2n^2 = 16
Dividing both sides by 2, we get:
n^2 = 8
Taking the square root of both sides, we find:
n = √8
n ≈ 2.83
Since n represents the shell number, we round it to the nearest whole number, which in this case is 3. Therefore, the shell with 16 orbitals is the third shell.