The number of electrons that fills a certain principle energy level equals ...

a-n

d-n²

b - 2n

c - 2n²

option c = 2n²

Explanation:

Principle energy levels are represented by n. The number of orbital per energy level are determine through n². While the number of electrons in per energy level are determine through 2n².

For example:

Principle energy level n number of orbitals n² number of electrons 2n².

1 1² = 1 2 (1) ² = 2

2 2² = 4 2 (2) ² = 8

3 3² = 9 2 (3) ² = 18

while the number of electrons in subshell can be determine through Aufbau principal. We know that there four subshells s, p, d and f. The maximum number of electrons in these subshells can be calculated by following formula:

2 (2l + 1)

and l = 0,1,2,3, ...

maximum numbers of electrons in s subshell are,

l=0

2 (2 (0) + 1)

2

so maximum electrons in s subshell are 2.

maximum numbers of electrons in p subshell are,

l = 1

2 (2 (1) + 1)

2 (2 + 1

6

so maximum electrons in p subshell are 6.

maximum numbers of electrons in d subshell are,

l = 2

2 (2 (2) + 1)

2 (4 + 1)

10

so maximum electrons in d subshell are 10.

maximum numbers of electrons in f subshell are,

l = 3

2 (2 (3) + 1)

2 (6 + 1)

14

so maximum electrons in f subshell are 14.