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.